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 Torricelli, F...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2011
|
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 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: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xix, 974 pages) |
| ISBN: | 9780511844195 |
| DOI: | 10.1017/CBO9780511844195 |
Internformat
MARC
| LEADER | 00000nmm a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV043943628 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 161206s2011 |||| o||u| ||||||eng d | ||
| 020 | |a 9780511844195 |c Online |9 978-0-511-84419-5 | ||
| 024 | 7 | |a 10.1017/CBO9780511844195 |2 doi | |
| 035 | |a (ZDB-20-CBO)CR9780511844195 | ||
| 035 | |a (OCoLC)839012612 | ||
| 035 | |a (DE-599)BVBBV043943628 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-92 | ||
| 082 | 0 | |a 510.72/2 |2 22 | |
| 084 | |a SG 590 |0 (DE-625)143069: |2 rvk | ||
| 100 | 1 | |a Roy, Ranjan |d 1948- |e Verfasser |4 aut | |
| 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 |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2011 | |
| 300 | |a 1 online resource (xix, 974 pages) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | |a Machine generated contents note: 1. Power series in fifteenth-century Kerala; 2. Sums of powers of integers; 3. Infinite product of Wallis; 4. The binomial theorem; 5. The rectification of curves; 6. Inequalities; 7. Geometric calculus; 8. The calculus of Newton and Leibniz; 9. De Analysi per Aequationes Infinitas; 10. Finite differences: interpolation and quadrature; 11. Series transformation by finite differences; 12. The Taylor series; 13. Integration of rational functions; 14. Difference equations; 15. Differential equations; 16. Series and products for elementary functions; 17. Solution of equations by radicals; 18. Symmetric functions; 19. Calculus of several variables; 20. Algebraic analysis: the calculus of operations; 21. Fourier series; 22. Trigonometric series after 1830; 23. The gamma function; 24. The asymptotic series for ln [Gamma] (x); 25. The Euler-Maclaurin summation formula; 26. L-series; 27. The hypergeometric series; 28. Orthogonal polynomials; 29. q-Series; 30. Partitions; 31. q-Series and q-orthogonal polynomials; 32. Primes in arithmetic progressions; 33. Distribution of primes: early results; 34. Invariant theory: Cayley and Sylvester; 35. Summability; 36. Elliptic functions: eighteenth century; 37. Elliptic functions: nineteenth century; 38. Irrational and transcendental numbers; 39. Value distribution theory; 40. Univalent functions; 41. Finite fields | |
| 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 | ||
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematics / Historiography | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druckausgabe |z 978-0-521-11470-7 |
| 856 | 4 | 0 | |u https://doi.org/10.1017/CBO9780511844195 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 912 | |a ZDB-20-CBO | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-029352599 | ||
| 966 | e | |u https://doi.org/10.1017/CBO9780511844195 |l BSB01 |p ZDB-20-CBO |q BSB_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/CBO9780511844195 |l FHN01 |p ZDB-20-CBO |q FHN_PDA_CBO |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804176887690297344 |
|---|---|
| any_adam_object | |
| author | Roy, Ranjan 1948- |
| author_facet | Roy, Ranjan 1948- |
| author_role | aut |
| author_sort | Roy, Ranjan 1948- |
| author_variant | r r rr |
| building | Verbundindex |
| bvnumber | BV043943628 |
| classification_rvk | SG 590 |
| collection | ZDB-20-CBO |
| contents | Machine generated contents note: 1. Power series in fifteenth-century Kerala; 2. Sums of powers of integers; 3. Infinite product of Wallis; 4. The binomial theorem; 5. The rectification of curves; 6. Inequalities; 7. Geometric calculus; 8. The calculus of Newton and Leibniz; 9. De Analysi per Aequationes Infinitas; 10. Finite differences: interpolation and quadrature; 11. Series transformation by finite differences; 12. The Taylor series; 13. Integration of rational functions; 14. Difference equations; 15. Differential equations; 16. Series and products for elementary functions; 17. Solution of equations by radicals; 18. Symmetric functions; 19. Calculus of several variables; 20. Algebraic analysis: the calculus of operations; 21. Fourier series; 22. Trigonometric series after 1830; 23. The gamma function; 24. The asymptotic series for ln [Gamma] (x); 25. The Euler-Maclaurin summation formula; 26. L-series; 27. The hypergeometric series; 28. Orthogonal polynomials; 29. q-Series; 30. Partitions; 31. q-Series and q-orthogonal polynomials; 32. Primes in arithmetic progressions; 33. Distribution of primes: early results; 34. Invariant theory: Cayley and Sylvester; 35. Summability; 36. Elliptic functions: eighteenth century; 37. Elliptic functions: nineteenth century; 38. Irrational and transcendental numbers; 39. Value distribution theory; 40. Univalent functions; 41. Finite fields |
| ctrlnum | (ZDB-20-CBO)CR9780511844195 (OCoLC)839012612 (DE-599)BVBBV043943628 |
| 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 |
| doi_str_mv | 10.1017/CBO9780511844195 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>04056nmm a2200421zc 4500</leader><controlfield tag="001">BV043943628</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">161206s2011 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780511844195</subfield><subfield code="c">Online</subfield><subfield code="9">978-0-511-84419-5</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1017/CBO9780511844195</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-20-CBO)CR9780511844195</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)839012612</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043943628</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-92</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510.72/2</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SG 590</subfield><subfield code="0">(DE-625)143069:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Roy, Ranjan</subfield><subfield code="d">1948-</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</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="264" ind1=" " ind2="1"><subfield code="a">Cambridge</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></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Title from publisher's bibliographic system (viewed on 05 Oct 2015)</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Machine generated contents note: 1. Power series in fifteenth-century Kerala; 2. Sums of powers of integers; 3. Infinite product of Wallis; 4. The binomial theorem; 5. The rectification of curves; 6. Inequalities; 7. Geometric calculus; 8. The calculus of Newton and Leibniz; 9. De Analysi per Aequationes Infinitas; 10. Finite differences: interpolation and quadrature; 11. Series transformation by finite differences; 12. The Taylor series; 13. Integration of rational functions; 14. Difference equations; 15. Differential equations; 16. Series and products for elementary functions; 17. Solution of equations by radicals; 18. Symmetric functions; 19. Calculus of several variables; 20. Algebraic analysis: the calculus of operations; 21. Fourier series; 22. Trigonometric series after 1830; 23. The gamma function; 24. The asymptotic series for ln [Gamma] (x); 25. The Euler-Maclaurin summation formula; 26. L-series; 27. The hypergeometric series; 28. Orthogonal polynomials; 29. q-Series; 30. Partitions; 31. q-Series and q-orthogonal polynomials; 32. Primes in arithmetic progressions; 33. Distribution of primes: early results; 34. Invariant theory: Cayley and Sylvester; 35. Summability; 36. Elliptic functions: eighteenth century; 37. Elliptic functions: nineteenth century; 38. Irrational and transcendental numbers; 39. Value distribution theory; 40. Univalent functions; 41. Finite fields</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></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics / Historiography</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druckausgabe</subfield><subfield code="z">978-0-521-11470-7</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1017/CBO9780511844195</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-20-CBO</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-029352599</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511844195</subfield><subfield code="l">BSB01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">BSB_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511844195</subfield><subfield code="l">FHN01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">FHN_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV043943628 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:19Z |
| institution | BVB |
| isbn | 9780511844195 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029352599 |
| oclc_num | 839012612 |
| open_access_boolean | |
| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (xix, 974 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Cambridge University Press |
| record_format | marc |
| spelling | Roy, Ranjan 1948- Verfasser aut Sources in the development of mathematics infinite series and products from the fifteenth to the twenty-first century Ranjan Roy Cambridge Cambridge University Press 2011 1 online resource (xix, 974 pages) txt rdacontent c rdamedia cr rdacarrier Title from publisher's bibliographic system (viewed on 05 Oct 2015) Machine generated contents note: 1. Power series in fifteenth-century Kerala; 2. Sums of powers of integers; 3. Infinite product of Wallis; 4. The binomial theorem; 5. The rectification of curves; 6. Inequalities; 7. Geometric calculus; 8. The calculus of Newton and Leibniz; 9. De Analysi per Aequationes Infinitas; 10. Finite differences: interpolation and quadrature; 11. Series transformation by finite differences; 12. The Taylor series; 13. Integration of rational functions; 14. Difference equations; 15. Differential equations; 16. Series and products for elementary functions; 17. Solution of equations by radicals; 18. Symmetric functions; 19. Calculus of several variables; 20. Algebraic analysis: the calculus of operations; 21. Fourier series; 22. Trigonometric series after 1830; 23. The gamma function; 24. The asymptotic series for ln [Gamma] (x); 25. The Euler-Maclaurin summation formula; 26. L-series; 27. The hypergeometric series; 28. Orthogonal polynomials; 29. q-Series; 30. Partitions; 31. q-Series and q-orthogonal polynomials; 32. Primes in arithmetic progressions; 33. Distribution of primes: early results; 34. Invariant theory: Cayley and Sylvester; 35. Summability; 36. Elliptic functions: eighteenth century; 37. Elliptic functions: nineteenth century; 38. Irrational and transcendental numbers; 39. Value distribution theory; 40. Univalent functions; 41. Finite fields 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 Mathematik Mathematics / Historiography Erscheint auch als Druckausgabe 978-0-521-11470-7 https://doi.org/10.1017/CBO9780511844195 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Roy, Ranjan 1948- Sources in the development of mathematics infinite series and products from the fifteenth to the twenty-first century Machine generated contents note: 1. Power series in fifteenth-century Kerala; 2. Sums of powers of integers; 3. Infinite product of Wallis; 4. The binomial theorem; 5. The rectification of curves; 6. Inequalities; 7. Geometric calculus; 8. The calculus of Newton and Leibniz; 9. De Analysi per Aequationes Infinitas; 10. Finite differences: interpolation and quadrature; 11. Series transformation by finite differences; 12. The Taylor series; 13. Integration of rational functions; 14. Difference equations; 15. Differential equations; 16. Series and products for elementary functions; 17. Solution of equations by radicals; 18. Symmetric functions; 19. Calculus of several variables; 20. Algebraic analysis: the calculus of operations; 21. Fourier series; 22. Trigonometric series after 1830; 23. The gamma function; 24. The asymptotic series for ln [Gamma] (x); 25. The Euler-Maclaurin summation formula; 26. L-series; 27. The hypergeometric series; 28. Orthogonal polynomials; 29. q-Series; 30. Partitions; 31. q-Series and q-orthogonal polynomials; 32. Primes in arithmetic progressions; 33. Distribution of primes: early results; 34. Invariant theory: Cayley and Sylvester; 35. Summability; 36. Elliptic functions: eighteenth century; 37. Elliptic functions: nineteenth century; 38. Irrational and transcendental numbers; 39. Value distribution theory; 40. Univalent functions; 41. Finite fields Mathematik Mathematics / Historiography |
| 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 | Mathematik Mathematics / Historiography |
| topic_facet | Mathematik Mathematics / Historiography |
| url | https://doi.org/10.1017/CBO9780511844195 |
| work_keys_str_mv | AT royranjan sourcesinthedevelopmentofmathematicsinfiniteseriesandproductsfromthefifteenthtothetwentyfirstcentury |