Bessel polynomials:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg ; New York
Springer-Verlag
1978
|
| Schriftenreihe: | Lecture notes in mathematics
698 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xiv, 182 Seiten Illustrationen |
| ISBN: | 3540091041 0387091041 |
Internformat
MARC
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| 100 | 1 | |a Grosswald, Emil |d 1912-1989 |0 (DE-588)119267551 |4 aut | |
| 245 | 1 | 0 | |a Bessel polynomials |c Emil Grosswald |
| 264 | 1 | |a Berlin ; Heidelberg ; New York |b Springer-Verlag |c 1978 | |
| 300 | |a xiv, 182 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 698 | |
| 650 | 4 | |a Bessel, Polynômes de | |
| 650 | 7 | |a Bessel-functies |2 gtt | |
| 650 | 4 | |a Bessel polynomials | |
| 650 | 0 | 7 | |a Bessel-Polynom |0 (DE-588)4144915-0 |2 gnd |9 rswk-swf |
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| 830 | 0 | |a Lecture notes in mathematics |v 698 |w (DE-604)BV000676446 |9 698 | |
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Datensatz im Suchindex
| _version_ | 1804116712133492736 |
|---|---|
| adam_text | TABLE OF CONTENTS
INTRODUCTION IX
PART I
CHAPTER 1 - Historic Sketch 1
CHAPTER 2 - Bessel Polynomials and Bessel Functions 4
Differential equations, their d-forms and their i-forms.
Polynomial solutions. Their relations to Bessel functions.
Generalized Bessel Polynomials.
CHAPTER 3 - Recurrence Relations 18
Recurrence relations for y »eT1» ( • Representation of BP by
determinants. Recurrence relations for the generalized
polynomials.
CHAPTER 4 - Moments and Orthogonality on the Unit Circle 25
Moment problems and solutions by Stieltjes, Tchebycheff,
Hamburger; the Bessel alternative. Weight function of the
generalized BP. Moments of the simple BP. Orthogonality
on the unit circle.
PART II
CHAPTER S - Relations of the BP to the classical orthonormal polynomials
and to other functions 34
BP as generalized hypergeometric functions, as limits of
Jacobi Polynomials, as Laguerre Polynomials; their
representation by Whittaker functions and by Lommel Polynomials.
CHAPTER 6 - Generating Functions 41
Generating functions and pseudogenerating functions. Results
of Krall and Frink, Burchnall, Al-Salam, Brafman, Carlitz,
and others. The theory of Lie groups and generating functions.
Results of Weisner, Chatterjea, Das, McBride, Chen and Feng,
and others. Different types of generating functions.
CHAPTER 7 - Formulas of Rodrigues Type 51
Methods of differential operators, of moments and of generating
functions. Combinatorial Lemmas.
CHAPTER 8 - The BP and Continued Fractions 59
The BP as partial quotients. Approximation of the exponential
function by ratios of BP.
CHAPTER 9 - Expansions of functions in series of BP 54
Formal expansions in series of the polynomials y (z;a,b), or
6 (z;a,b). The Boas-Buck theory of generalized Appell Polynomials.
Convergence and summability of expansions in BP. Applications
to expansions of powers and of exponentials.
PART III
CHAPTER 10 - Properties of the zeros of BP 75
Location of zeros. Results of Burchnall, Grosswald, Dickinson,
Agarwal, Barnes, van Rossum, Nasif, Parodi, McCarthy, Dofev,
Wragg and Underhill, Saff and Varga. Olver s theorem. Laguerre s
Theorem. Results of Ismail and Kelker. Sums of powers of
the zeros.
VIII
CHAPTER 11 - On the algebraic irreducibility of the BP 99
Theorems of Dumas, Eisenstein, and Breusch. Newton Polygon.
Degrees of possible factors. Cases of irreducibility. Schemes
of factorization. Two conjectures.
CHAPTER 12 - The Galois Group of BP 116
Theorems of Schur, Dedekind, Jordan, Cauchy, and Burnside.
Resolvent and Discriminant. The Galois Group of the
irreducible BP is the symmetric group. Details of the case n = 8.
CHAPTER 13 - Asymptotic properties of the BP 124
Case of n constant, z ¦+• 0. Case of constant z, n ¦*¦ «°.
Results of Grosswald, Obreshkov, Dofev.
PART IV
CHAPTER 14 - Applications , 131
The irrationality of er (r rational) and of it2. Solution of
the wave equation. The infinite divisibility of the Student
t-distribution. Bernstein s theorem. Electrical networks
with maximally flat delay. The inversion of the Laplace
transform. Salzer s theorem.
CHAPTER 15 - Miscellanea 150
Mention of the work by many authors, not discussed in the
preceding chapters.
APPENDIX - Some open problems related to BP 162
BIBLIOGRAPHY of books and papers related to BP 164
BIBLIOGRAPHY of literature not directly related to BP 171
SUBJECT INDEX 175
NAME INDEX 179
PARTIAL LIST OF SYMBOLS 181
|
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| classification_rvk | SI 850 |
| ctrlnum | (OCoLC)4593623 (DE-599)BVBBV002255426 |
| dewey-full | 515/.53 510/.8 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis 510 - Mathematics |
| dewey-raw | 515/.53 510/.8 |
| dewey-search | 515/.53 510/.8 |
| dewey-sort | 3515 253 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002255426 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:42:52Z |
| institution | BVB |
| isbn | 3540091041 0387091041 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001482138 |
| oclc_num | 4593623 |
| open_access_boolean | |
| owner | DE-12 DE-91G DE-BY-TUM DE-384 DE-473 DE-BY-UBG DE-739 DE-355 DE-BY-UBR DE-20 DE-824 DE-29T DE-19 DE-BY-UBM DE-706 DE-83 DE-188 DE-11 |
| owner_facet | DE-12 DE-91G DE-BY-TUM DE-384 DE-473 DE-BY-UBG DE-739 DE-355 DE-BY-UBR DE-20 DE-824 DE-29T DE-19 DE-BY-UBM DE-706 DE-83 DE-188 DE-11 |
| physical | xiv, 182 Seiten Illustrationen |
| publishDate | 1978 |
| publishDateSearch | 1978 |
| publishDateSort | 1978 |
| publisher | Springer-Verlag |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Grosswald, Emil 1912-1989 (DE-588)119267551 aut Bessel polynomials Emil Grosswald Berlin ; Heidelberg ; New York Springer-Verlag 1978 xiv, 182 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 698 Bessel, Polynômes de Bessel-functies gtt Bessel polynomials Bessel-Polynom (DE-588)4144915-0 gnd rswk-swf Bessel-Polynom (DE-588)4144915-0 s DE-604 Erscheint auch als Online-Ausgabe 978-3-540-09104-2 Lecture notes in mathematics 698 (DE-604)BV000676446 698 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001482138&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Grosswald, Emil 1912-1989 Bessel polynomials Lecture notes in mathematics Bessel, Polynômes de Bessel-functies gtt Bessel polynomials Bessel-Polynom (DE-588)4144915-0 gnd |
| subject_GND | (DE-588)4144915-0 |
| title | Bessel polynomials |
| title_auth | Bessel polynomials |
| title_exact_search | Bessel polynomials |
| title_full | Bessel polynomials Emil Grosswald |
| title_fullStr | Bessel polynomials Emil Grosswald |
| title_full_unstemmed | Bessel polynomials Emil Grosswald |
| title_short | Bessel polynomials |
| title_sort | bessel polynomials |
| topic | Bessel, Polynômes de Bessel-functies gtt Bessel polynomials Bessel-Polynom (DE-588)4144915-0 gnd |
| topic_facet | Bessel, Polynômes de Bessel-functies Bessel polynomials Bessel-Polynom |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001482138&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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