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| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783642050145 |
|
978-3-642-05014-5 |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA351 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
515.5 |
| Edition number |
23 |
| 264 #1 - |
|---|
| -- |
Berlin, Heidelberg : |
| -- |
Springer Berlin Heidelberg, |
| -- |
2010. |
| 912 ## - |
|---|
| -- |
ZDB-2-SMA |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Koekoek, Roelof. |
| Relator term |
author. |
| 245 10 - IMMEDIATE SOURCE OF ACQUISITION NOTE |
|---|
| Title |
Hypergeometric Orthogonal Polynomials and Their q-Analogues |
| Medium |
[electronic resource] / |
| Statement of responsibility, etc |
by Roelof Koekoek, Peter A. Lesky, René F. Swarttouw. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
XIX, 578 p. 2 illus. |
| Other physical details |
online resource. |
| 440 1# - SERIES STATEMENT/ADDED ENTRY--TITLE |
|---|
| Title |
Springer Monographs in Mathematics, |
| International Standard Serial Number |
1439-7382 |
| 505 0# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
Definitions and Miscellaneous Formulas -- Classical orthogonal polynomials -- Orthogonal Polynomial Solutions of Differential Equations -- Orthogonal Polynomial Solutions of Real Difference Equations -- Orthogonal Polynomial Solutions of Complex Difference Equations -- Orthogonal Polynomial Solutions in x(x+u) of Real Difference Equations -- Orthogonal Polynomial Solutions in z(z+u) of Complex Difference Equations -- Hypergeometric Orthogonal Polynomials -- Polynomial Solutions of Eigenvalue Problems -- Classical q-orthogonal polynomials -- Orthogonal Polynomial Solutions of q-Difference Equations -- Orthogonal Polynomial Solutions in q?x of q-Difference Equations -- Orthogonal Polynomial Solutions in q?x+uqx of Real. |
| 520 ## - SUMMARY, ETC. |
|---|
| Summary, etc |
The very classical orthogonal polynomials named after Hermite, Laguerre and Jacobi, satisfy many common properties. For instance, they satisfy a second-order differential equation with polynomial coefficients and they can be expressed in terms of a hypergeometric function. Replacing the differential equation by a second-order difference equation results in (discrete) orthogonal polynomial solutions with similar properties. Generalizations of these difference equations, in terms of Hahn's q-difference operator, lead to both continuous and discrete orthogonal polynomials with similar properties. For instance, they can be expressed in terms of (basic) hypergeometric functions. Based on Favard's theorem, the authors first classify all families of orthogonal polynomials satisfying a second-order differential or difference equation with polynomial coefficients. Together with the concept of duality this leads to the families of hypergeometric orthogonal polynomials belonging to the Askey scheme. For each family they list the most important properties and they indicate the (limit) relations. Furthermore the authors classify all q-orthogonal polynomials satisfying a second-order q-difference equation based on Hahn's q-operator. Together with the concept of duality this leads to the families of basic hypergeometric orthogonal polynomials which can be arranged in a q-analogue of the Askey scheme. Again, for each family they list the most important properties, the (limit) relations between the various families and the limit relations (for q --> 1) to the classical hypergeometric orthogonal polynomials belonging to the Askey scheme. These (basic) hypergeometric orthogonal polynomials have several applications in various areas of mathematics and (quantum) physics such as approximation theory, asymptotics, birth and death processes, probability and statistics, coding theory and combinatorics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematics. |
|
|---|
| Topical term or geographic name as entry element |
Functions, special. |
|
|---|
| Topical term or geographic name as entry element |
Mathematics. |
|
|---|
| Topical term or geographic name as entry element |
Special Functions. |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
|---|
| Personal name |
Lesky, Peter A. |
| Relator term |
author. |
|
|---|
| Personal name |
Swarttouw, René F. |
| Relator term |
author. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
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| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
|---|
| Title |
Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| Display text |
Printed edition: |
| International Standard Book Number |
9783642050138 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Uniform Resource Identifier |
http://dx.doi.org/10.1007/978-3-642-05014-5 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
|---|
| Source of classification or shelving scheme |
|
| Item type |
E-Book |
