Sources in the development of mathematics :: infinite series and products from the fifteenth to the twenty-first century /
"The discovery of infinite products by Wallis and infinite series by Newton marked the beginning of the modern mathematical era. It allowed Newton to solve the problem of finding areas under curves defined by algebraic equations, an achievement beyond the scope of the earlier methods of Torrice...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
2011.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "The discovery of infinite products by Wallis and infinite series by Newton marked the beginning of the modern mathematical era. It allowed Newton to solve the problem of finding areas under curves defined by algebraic equations, an achievement beyond the scope of the earlier methods of Torricelli, Fermat and Pascal. While Newton and his contemporaries, including Leibniz and the Bernoullis, concentrated on mathematical analysis and physics, Euler's prodigious accomplishments demonstrated that series and products could also address problems in algebra, combinatorics and number theory. In this book, Ranjan Roy describes many facets of the discovery and use of infinite series and products as worked out by their originators, including mathematicians from Asia, Europe and America. The text provides context and motivation for these discoveries, with many detailed proofs, offering a valuable perspective on modern mathematics. Mathematicians, mathematics students, physicists and engineers will all read this book with benefit and enjoyment"-- |
| Beschreibung: | 1 online resource (xix, 974 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 943-958) and index. |
| ISBN: | 9781139127523 1139127527 9780521114707 0521114705 9781139136228 1139136224 9781139114691 1139114697 9781139116862 113911686X 1316086585 9781316086582 1139635514 9781139635516 1283295849 9781283295840 1139122606 9781139122603 9786613295842 6613295841 0511844190 9780511844195 1139112503 9781139112505 |
Internformat
MARC
| LEADER | 00000cam a2200000 a 4500 | ||
|---|---|---|---|
| 001 | ZDB-4-EBA-ocn770009966 | ||
| 003 | OCoLC | ||
| 005 | 20241004212047.0 | ||
| 006 | m o d | ||
| 007 | cr cnu---unuuu | ||
| 008 | 120103s2011 enka ob 001 0 eng d | ||
| 010 | |a 2011012265 | ||
| 040 | |a N$T |b eng |e pn |c N$T |d GGVRL |d CDX |d YDXCP |d E7B |d REDDC |d OCLCQ |d DEBSZ |d OCLCQ |d COO |d EBLCP |d UPP |d OCLCF |d OCLCQ |d UAB |d OCLCQ |d LND |d OCLCQ |d COCUF |d CNNOR |d STF |d MERUC |d ZCU |d ICG |d INT |d K6U |d LOA |d VT2 |d U3W |d CNCEN |d OCLCQ |d WYU |d G3B |d LVT |d S9I |d OCLCQ |d DKC |d OCLCQ |d UKAHL |d OCLCQ |d D6H |d AU@ |d A6Q |d UHL |d OCLCQ |d UKCRE |d AJS |d OCLCQ |d QGK |d OCLCO |d AAA |d OCLCQ |d BRX |d OCLCQ |d OCLCO |d OCLCL |d SFB |d OCLCQ | ||
| 019 | |a 759007155 |a 764337494 |a 769341828 |a 1038402618 |a 1042962418 |a 1043673412 |a 1059043545 |a 1059244814 |a 1066680128 |a 1078492899 |a 1081232916 |a 1084428761 |a 1105764544 |a 1153541521 |a 1228599422 |a 1259202179 | ||
| 020 | |a 9781139127523 |q (electronic bk.) | ||
| 020 | |a 1139127527 |q (electronic bk.) | ||
| 020 | |a 9780521114707 |q (electronic bk.) | ||
| 020 | |a 0521114705 |q (electronic bk.) | ||
| 020 | |a 9781139136228 |q (electronic book) | ||
| 020 | |a 1139136224 |q (electronic book) | ||
| 020 | |a 9781139114691 | ||
| 020 | |a 1139114697 | ||
| 020 | |a 9781139116862 | ||
| 020 | |a 113911686X | ||
| 020 | |a 1316086585 | ||
| 020 | |a 9781316086582 | ||
| 020 | |a 1139635514 | ||
| 020 | |a 9781139635516 | ||
| 020 | |a 1283295849 | ||
| 020 | |a 9781283295840 | ||
| 020 | |a 1139122606 | ||
| 020 | |a 9781139122603 | ||
| 020 | |a 9786613295842 | ||
| 020 | |a 6613295841 | ||
| 020 | |a 0511844190 | ||
| 020 | |a 9780511844195 | ||
| 020 | |a 1139112503 | ||
| 020 | |a 9781139112505 | ||
| 024 | 8 | |a 9786613295842 | |
| 035 | |a (OCoLC)770009966 |z (OCoLC)759007155 |z (OCoLC)764337494 |z (OCoLC)769341828 |z (OCoLC)1038402618 |z (OCoLC)1042962418 |z (OCoLC)1043673412 |z (OCoLC)1059043545 |z (OCoLC)1059244814 |z (OCoLC)1066680128 |z (OCoLC)1078492899 |z (OCoLC)1081232916 |z (OCoLC)1084428761 |z (OCoLC)1105764544 |z (OCoLC)1153541521 |z (OCoLC)1228599422 |z (OCoLC)1259202179 | ||
| 037 | |a 329584 |b MIL | ||
| 050 | 4 | |a QA21 |b .R69 2011eb | |
| 072 | 7 | |a MAT |x 027000 |2 bisacsh | |
| 082 | 7 | |a 510.72/2 |2 22 | |
| 084 | |a MAT000000 |2 bisacsh | ||
| 049 | |a MAIN | ||
| 100 | 1 | |a Roy, Ranjan, |d 1948- |1 https://id.oclc.org/worldcat/entity/E39PCjDqJKXrRtrjpXfBBVPVJC |0 http://id.loc.gov/authorities/names/n98047180 | |
| 245 | 1 | 0 | |a Sources in the development of mathematics : |b infinite series and products from the fifteenth to the twenty-first century / |c Ranjan Roy. |
| 260 | |a Cambridge ; |a New York : |b Cambridge University Press, |c 2011. | ||
| 300 | |a 1 online resource (xix, 974 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a data file | ||
| 520 | |a "The discovery of infinite products by Wallis and infinite series by Newton marked the beginning of the modern mathematical era. It allowed Newton to solve the problem of finding areas under curves defined by algebraic equations, an achievement beyond the scope of the earlier methods of Torricelli, Fermat and Pascal. While Newton and his contemporaries, including Leibniz and the Bernoullis, concentrated on mathematical analysis and physics, Euler's prodigious accomplishments demonstrated that series and products could also address problems in algebra, combinatorics and number theory. In this book, Ranjan Roy describes many facets of the discovery and use of infinite series and products as worked out by their originators, including mathematicians from Asia, Europe and America. The text provides context and motivation for these discoveries, with many detailed proofs, offering a valuable perspective on modern mathematics. Mathematicians, mathematics students, physicists and engineers will all read this book with benefit and enjoyment"-- |c Provided by publisher | ||
| 504 | |a Includes bibliographical references (pages 943-958) and index. | ||
| 505 | 0 | |a Power series in fifteenth-century Kerala -- Sums of powers of integers -- Infinite product of Wallis -- The binomial theorem -- The rectification of curves -- Inequalities -- Geometric calculus -- The calculus of Newton and Leibniz -- De Analysi per Aequationes Infinitas -- Finite differences : interpolation and quadrature -- Series transformation by finite differences -- The Taylor series -- Integration of rational functions -- Difference equations -- Differential equations -- Series and products for elementary functions -- Solution of equations by radicals -- Symmetric functions -- Calculus of several variables -- Algebraic analysis: the calculus of operations -- Fourier series -- Trigonometric series after 1830 -- The gamma function -- The asymptotic series for ln [Gamma] (x) -- The Euler-Maclaurin summation formula -- L-series -- The hypergeometric series -- Orthogonal polynomials -- q-Series -- Partitions -- q-Series and q-orthogonal polynomials -- Primes in arithmetic progressions -- Distribution of primes : early results -- Invariant theory : Cayley and Sylvester -- Summability -- Elliptic functions : eighteenth century -- Elliptic functions : nineteenth century -- Irrational and transcendental numbers -- Value distribution theory -- Univalent functions -- Finite fields. | |
| 588 | 0 | |a Print version record. | |
| 546 | |a English. | ||
| 650 | 0 | |a Mathematics |x Historiography. |0 http://id.loc.gov/authorities/subjects/sh85082149 | |
| 650 | 7 | |a MATHEMATICS |x General. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Research. |2 bisacsh | |
| 650 | 7 | |a Mathematics |x Historiography |2 fast | |
| 758 | |i has work: |a Sources in the development of mathematics (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFwxbmMfmBCb93c97c4C33 |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Roy, Ranjan, 1948- |t Sources in the development of mathematics. |d Cambridge ; New York : Cambridge University Press, 2011 |z 9780521114707 |w (DLC) 2011012265 |w (OCoLC)715284772 |
| 856 | 4 | 0 | |l FWS01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=399311 |3 Volltext |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH34202020 | ||
| 938 | |a Askews and Holts Library Services |b ASKH |n AH33230419 | ||
| 938 | |a Askews and Holts Library Services |b ASKH |n AH26478617 | ||
| 938 | |a Coutts Information Services |b COUT |n 19724644 | ||
| 938 | |a EBL - Ebook Library |b EBLB |n EBL775124 | ||
| 938 | |a ebrary |b EBRY |n ebr10502794 | ||
| 938 | |a EBSCOhost |b EBSC |n 399311 | ||
| 938 | |a Cengage Learning |b GVRL |n gal9781139136228 | ||
| 938 | |a YBP Library Services |b YANK |n 7245285 | ||
| 938 | |a YBP Library Services |b YANK |n 7302873 | ||
| 938 | |a YBP Library Services |b YANK |n 7353959 | ||
| 938 | |a YBP Library Services |b YANK |n 9247830 | ||
| 938 | |a YBP Library Services |b YANK |n 7205426 | ||
| 994 | |a 92 |b GEBAY | ||
| 912 | |a ZDB-4-EBA | ||
| 049 | |a DE-863 | ||
Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn770009966 |
|---|---|
| _version_ | 1816881781551398912 |
| adam_text | |
| any_adam_object | |
| author | Roy, Ranjan, 1948- |
| author_GND | http://id.loc.gov/authorities/names/n98047180 |
| author_facet | Roy, Ranjan, 1948- |
| author_role | |
| author_sort | Roy, Ranjan, 1948- |
| author_variant | r r rr |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA21 |
| callnumber-raw | QA21 .R69 2011eb |
| callnumber-search | QA21 .R69 2011eb |
| callnumber-sort | QA 221 R69 42011EB |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | Power series in fifteenth-century Kerala -- Sums of powers of integers -- Infinite product of Wallis -- The binomial theorem -- The rectification of curves -- Inequalities -- Geometric calculus -- The calculus of Newton and Leibniz -- De Analysi per Aequationes Infinitas -- Finite differences : interpolation and quadrature -- Series transformation by finite differences -- The Taylor series -- Integration of rational functions -- Difference equations -- Differential equations -- Series and products for elementary functions -- Solution of equations by radicals -- Symmetric functions -- Calculus of several variables -- Algebraic analysis: the calculus of operations -- Fourier series -- Trigonometric series after 1830 -- The gamma function -- The asymptotic series for ln [Gamma] (x) -- The Euler-Maclaurin summation formula -- L-series -- The hypergeometric series -- Orthogonal polynomials -- q-Series -- Partitions -- q-Series and q-orthogonal polynomials -- Primes in arithmetic progressions -- Distribution of primes : early results -- Invariant theory : Cayley and Sylvester -- Summability -- Elliptic functions : eighteenth century -- Elliptic functions : nineteenth century -- Irrational and transcendental numbers -- Value distribution theory -- Univalent functions -- Finite fields. |
| ctrlnum | (OCoLC)770009966 |
| dewey-full | 510.72/2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510.72/2 |
| dewey-search | 510.72/2 |
| dewey-sort | 3510.72 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>06772cam a2200925 a 4500</leader><controlfield tag="001">ZDB-4-EBA-ocn770009966</controlfield><controlfield tag="003">OCoLC</controlfield><controlfield tag="005">20241004212047.0</controlfield><controlfield tag="006">m o d </controlfield><controlfield tag="007">cr cnu---unuuu</controlfield><controlfield tag="008">120103s2011 enka ob 001 0 eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a"> 2011012265</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">N$T</subfield><subfield code="b">eng</subfield><subfield code="e">pn</subfield><subfield code="c">N$T</subfield><subfield code="d">GGVRL</subfield><subfield code="d">CDX</subfield><subfield code="d">YDXCP</subfield><subfield code="d">E7B</subfield><subfield code="d">REDDC</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">DEBSZ</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">COO</subfield><subfield code="d">EBLCP</subfield><subfield code="d">UPP</subfield><subfield code="d">OCLCF</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">UAB</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">LND</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">COCUF</subfield><subfield code="d">CNNOR</subfield><subfield code="d">STF</subfield><subfield code="d">MERUC</subfield><subfield code="d">ZCU</subfield><subfield code="d">ICG</subfield><subfield code="d">INT</subfield><subfield code="d">K6U</subfield><subfield code="d">LOA</subfield><subfield code="d">VT2</subfield><subfield code="d">U3W</subfield><subfield code="d">CNCEN</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">WYU</subfield><subfield code="d">G3B</subfield><subfield code="d">LVT</subfield><subfield code="d">S9I</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">DKC</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">UKAHL</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">D6H</subfield><subfield code="d">AU@</subfield><subfield code="d">A6Q</subfield><subfield code="d">UHL</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">UKCRE</subfield><subfield code="d">AJS</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">QGK</subfield><subfield code="d">OCLCO</subfield><subfield code="d">AAA</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">BRX</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCL</subfield><subfield code="d">SFB</subfield><subfield code="d">OCLCQ</subfield></datafield><datafield tag="019" ind1=" " ind2=" "><subfield code="a">759007155</subfield><subfield code="a">764337494</subfield><subfield code="a">769341828</subfield><subfield code="a">1038402618</subfield><subfield code="a">1042962418</subfield><subfield code="a">1043673412</subfield><subfield code="a">1059043545</subfield><subfield code="a">1059244814</subfield><subfield code="a">1066680128</subfield><subfield code="a">1078492899</subfield><subfield code="a">1081232916</subfield><subfield code="a">1084428761</subfield><subfield code="a">1105764544</subfield><subfield code="a">1153541521</subfield><subfield code="a">1228599422</subfield><subfield code="a">1259202179</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781139127523</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1139127527</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780521114707</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0521114705</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781139136228</subfield><subfield code="q">(electronic book)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1139136224</subfield><subfield code="q">(electronic book)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781139114691</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1139114697</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781139116862</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">113911686X</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1316086585</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781316086582</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1139635514</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781139635516</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1283295849</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781283295840</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1139122606</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781139122603</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9786613295842</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">6613295841</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0511844190</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780511844195</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1139112503</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781139112505</subfield></datafield><datafield tag="024" ind1="8" ind2=" "><subfield code="a">9786613295842</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)770009966</subfield><subfield code="z">(OCoLC)759007155</subfield><subfield code="z">(OCoLC)764337494</subfield><subfield code="z">(OCoLC)769341828</subfield><subfield code="z">(OCoLC)1038402618</subfield><subfield code="z">(OCoLC)1042962418</subfield><subfield code="z">(OCoLC)1043673412</subfield><subfield code="z">(OCoLC)1059043545</subfield><subfield code="z">(OCoLC)1059244814</subfield><subfield code="z">(OCoLC)1066680128</subfield><subfield code="z">(OCoLC)1078492899</subfield><subfield code="z">(OCoLC)1081232916</subfield><subfield code="z">(OCoLC)1084428761</subfield><subfield code="z">(OCoLC)1105764544</subfield><subfield code="z">(OCoLC)1153541521</subfield><subfield code="z">(OCoLC)1228599422</subfield><subfield code="z">(OCoLC)1259202179</subfield></datafield><datafield tag="037" ind1=" " ind2=" "><subfield code="a">329584</subfield><subfield code="b">MIL</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA21</subfield><subfield code="b">.R69 2011eb</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">027000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">510.72/2</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT000000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Roy, Ranjan,</subfield><subfield code="d">1948-</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCjDqJKXrRtrjpXfBBVPVJC</subfield><subfield code="0">http://id.loc.gov/authorities/names/n98047180</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Sources in the development of mathematics :</subfield><subfield code="b">infinite series and products from the fifteenth to the twenty-first century /</subfield><subfield code="c">Ranjan Roy.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">Cambridge ;</subfield><subfield code="a">New York :</subfield><subfield code="b">Cambridge University Press,</subfield><subfield code="c">2011.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xix, 974 pages) :</subfield><subfield code="b">illustrations</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="347" ind1=" " ind2=" "><subfield code="a">data file</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">"The discovery of infinite products by Wallis and infinite series by Newton marked the beginning of the modern mathematical era. It allowed Newton to solve the problem of finding areas under curves defined by algebraic equations, an achievement beyond the scope of the earlier methods of Torricelli, Fermat and Pascal. While Newton and his contemporaries, including Leibniz and the Bernoullis, concentrated on mathematical analysis and physics, Euler's prodigious accomplishments demonstrated that series and products could also address problems in algebra, combinatorics and number theory. In this book, Ranjan Roy describes many facets of the discovery and use of infinite series and products as worked out by their originators, including mathematicians from Asia, Europe and America. The text provides context and motivation for these discoveries, with many detailed proofs, offering a valuable perspective on modern mathematics. Mathematicians, mathematics students, physicists and engineers will all read this book with benefit and enjoyment"--</subfield><subfield code="c">Provided by publisher</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (pages 943-958) and index.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Power series in fifteenth-century Kerala -- Sums of powers of integers -- Infinite product of Wallis -- The binomial theorem -- The rectification of curves -- Inequalities -- Geometric calculus -- The calculus of Newton and Leibniz -- De Analysi per Aequationes Infinitas -- Finite differences : interpolation and quadrature -- Series transformation by finite differences -- The Taylor series -- Integration of rational functions -- Difference equations -- Differential equations -- Series and products for elementary functions -- Solution of equations by radicals -- Symmetric functions -- Calculus of several variables -- Algebraic analysis: the calculus of operations -- Fourier series -- Trigonometric series after 1830 -- The gamma function -- The asymptotic series for ln [Gamma] (x) -- The Euler-Maclaurin summation formula -- L-series -- The hypergeometric series -- Orthogonal polynomials -- q-Series -- Partitions -- q-Series and q-orthogonal polynomials -- Primes in arithmetic progressions -- Distribution of primes : early results -- Invariant theory : Cayley and Sylvester -- Summability -- Elliptic functions : eighteenth century -- Elliptic functions : nineteenth century -- Irrational and transcendental numbers -- Value distribution theory -- Univalent functions -- Finite fields.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">English.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Mathematics</subfield><subfield code="x">Historiography.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85082149</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">General.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Research.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Mathematics</subfield><subfield code="x">Historiography</subfield><subfield code="2">fast</subfield></datafield><datafield tag="758" ind1=" " ind2=" "><subfield code="i">has work:</subfield><subfield code="a">Sources in the development of mathematics (Text)</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCFwxbmMfmBCb93c97c4C33</subfield><subfield code="4">https://id.oclc.org/worldcat/ontology/hasWork</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Roy, Ranjan, 1948-</subfield><subfield code="t">Sources in the development of mathematics.</subfield><subfield code="d">Cambridge ; New York : Cambridge University Press, 2011</subfield><subfield code="z">9780521114707</subfield><subfield code="w">(DLC) 2011012265</subfield><subfield code="w">(OCoLC)715284772</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=399311</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH34202020</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH33230419</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH26478617</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Coutts Information Services</subfield><subfield code="b">COUT</subfield><subfield code="n">19724644</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBL - Ebook Library</subfield><subfield code="b">EBLB</subfield><subfield code="n">EBL775124</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ebrary</subfield><subfield code="b">EBRY</subfield><subfield code="n">ebr10502794</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">399311</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Cengage Learning</subfield><subfield code="b">GVRL</subfield><subfield code="n">gal9781139136228</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">7245285</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">7302873</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">7353959</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">9247830</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">7205426</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-863</subfield></datafield></record></collection> |
| id | ZDB-4-EBA-ocn770009966 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:18:10Z |
| institution | BVB |
| isbn | 9781139127523 1139127527 9780521114707 0521114705 9781139136228 1139136224 9781139114691 1139114697 9781139116862 113911686X 1316086585 9781316086582 1139635514 9781139635516 1283295849 9781283295840 1139122606 9781139122603 9786613295842 6613295841 0511844190 9780511844195 1139112503 9781139112505 |
| language | English |
| lccn | 2011012265 |
| oclc_num | 770009966 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xix, 974 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Cambridge University Press, |
| record_format | marc |
| spelling | Roy, Ranjan, 1948- https://id.oclc.org/worldcat/entity/E39PCjDqJKXrRtrjpXfBBVPVJC http://id.loc.gov/authorities/names/n98047180 Sources in the development of mathematics : infinite series and products from the fifteenth to the twenty-first century / Ranjan Roy. Cambridge ; New York : Cambridge University Press, 2011. 1 online resource (xix, 974 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier data file "The discovery of infinite products by Wallis and infinite series by Newton marked the beginning of the modern mathematical era. It allowed Newton to solve the problem of finding areas under curves defined by algebraic equations, an achievement beyond the scope of the earlier methods of Torricelli, Fermat and Pascal. While Newton and his contemporaries, including Leibniz and the Bernoullis, concentrated on mathematical analysis and physics, Euler's prodigious accomplishments demonstrated that series and products could also address problems in algebra, combinatorics and number theory. In this book, Ranjan Roy describes many facets of the discovery and use of infinite series and products as worked out by their originators, including mathematicians from Asia, Europe and America. The text provides context and motivation for these discoveries, with many detailed proofs, offering a valuable perspective on modern mathematics. Mathematicians, mathematics students, physicists and engineers will all read this book with benefit and enjoyment"-- Provided by publisher Includes bibliographical references (pages 943-958) and index. Power series in fifteenth-century Kerala -- Sums of powers of integers -- Infinite product of Wallis -- The binomial theorem -- The rectification of curves -- Inequalities -- Geometric calculus -- The calculus of Newton and Leibniz -- De Analysi per Aequationes Infinitas -- Finite differences : interpolation and quadrature -- Series transformation by finite differences -- The Taylor series -- Integration of rational functions -- Difference equations -- Differential equations -- Series and products for elementary functions -- Solution of equations by radicals -- Symmetric functions -- Calculus of several variables -- Algebraic analysis: the calculus of operations -- Fourier series -- Trigonometric series after 1830 -- The gamma function -- The asymptotic series for ln [Gamma] (x) -- The Euler-Maclaurin summation formula -- L-series -- The hypergeometric series -- Orthogonal polynomials -- q-Series -- Partitions -- q-Series and q-orthogonal polynomials -- Primes in arithmetic progressions -- Distribution of primes : early results -- Invariant theory : Cayley and Sylvester -- Summability -- Elliptic functions : eighteenth century -- Elliptic functions : nineteenth century -- Irrational and transcendental numbers -- Value distribution theory -- Univalent functions -- Finite fields. Print version record. English. Mathematics Historiography. http://id.loc.gov/authorities/subjects/sh85082149 MATHEMATICS General. bisacsh MATHEMATICS Research. bisacsh Mathematics Historiography fast has work: Sources in the development of mathematics (Text) https://id.oclc.org/worldcat/entity/E39PCFwxbmMfmBCb93c97c4C33 https://id.oclc.org/worldcat/ontology/hasWork Print version: Roy, Ranjan, 1948- Sources in the development of mathematics. Cambridge ; New York : Cambridge University Press, 2011 9780521114707 (DLC) 2011012265 (OCoLC)715284772 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=399311 Volltext |
| spellingShingle | Roy, Ranjan, 1948- Sources in the development of mathematics : infinite series and products from the fifteenth to the twenty-first century / Power series in fifteenth-century Kerala -- Sums of powers of integers -- Infinite product of Wallis -- The binomial theorem -- The rectification of curves -- Inequalities -- Geometric calculus -- The calculus of Newton and Leibniz -- De Analysi per Aequationes Infinitas -- Finite differences : interpolation and quadrature -- Series transformation by finite differences -- The Taylor series -- Integration of rational functions -- Difference equations -- Differential equations -- Series and products for elementary functions -- Solution of equations by radicals -- Symmetric functions -- Calculus of several variables -- Algebraic analysis: the calculus of operations -- Fourier series -- Trigonometric series after 1830 -- The gamma function -- The asymptotic series for ln [Gamma] (x) -- The Euler-Maclaurin summation formula -- L-series -- The hypergeometric series -- Orthogonal polynomials -- q-Series -- Partitions -- q-Series and q-orthogonal polynomials -- Primes in arithmetic progressions -- Distribution of primes : early results -- Invariant theory : Cayley and Sylvester -- Summability -- Elliptic functions : eighteenth century -- Elliptic functions : nineteenth century -- Irrational and transcendental numbers -- Value distribution theory -- Univalent functions -- Finite fields. Mathematics Historiography. http://id.loc.gov/authorities/subjects/sh85082149 MATHEMATICS General. bisacsh MATHEMATICS Research. bisacsh Mathematics Historiography fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85082149 |
| title | Sources in the development of mathematics : infinite series and products from the fifteenth to the twenty-first century / |
| title_auth | Sources in the development of mathematics : infinite series and products from the fifteenth to the twenty-first century / |
| title_exact_search | Sources in the development of mathematics : infinite series and products from the fifteenth to the twenty-first century / |
| title_full | Sources in the development of mathematics : infinite series and products from the fifteenth to the twenty-first century / Ranjan Roy. |
| title_fullStr | Sources in the development of mathematics : infinite series and products from the fifteenth to the twenty-first century / Ranjan Roy. |
| title_full_unstemmed | Sources in the development of mathematics : infinite series and products from the fifteenth to the twenty-first century / Ranjan Roy. |
| title_short | Sources in the development of mathematics : |
| title_sort | sources in the development of mathematics infinite series and products from the fifteenth to the twenty first century |
| title_sub | infinite series and products from the fifteenth to the twenty-first century / |
| topic | Mathematics Historiography. http://id.loc.gov/authorities/subjects/sh85082149 MATHEMATICS General. bisacsh MATHEMATICS Research. bisacsh Mathematics Historiography fast |
| topic_facet | Mathematics Historiography. MATHEMATICS General. MATHEMATICS Research. Mathematics Historiography |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=399311 |
| work_keys_str_mv | AT royranjan sourcesinthedevelopmentofmathematicsinfiniteseriesandproductsfromthefifteenthtothetwentyfirstcentury |