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21: 18.2 General Orthogonal Polynomials

§18.2 General Orthogonal Polynomials

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Orthogonality on Intervals

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Orthogonality on General Sets

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22: 18.42 Software

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CAOP (website). Computer Algebra and Orthogonal Polynomials.

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23: 31.9 Orthogonality

§31.9 Orthogonality

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§31.9(i) Single Orthogonality

… ►For corresponding orthogonality relations for Heun functions (§31.4) and Heun polynomials (§31.5), see Lambe and Ward (1934), Erdélyi (1944), Sleeman (1966a), and Ronveaux (1995, Part A, pp. 59–64). ►

§31.9(ii) Double Orthogonality

… ►For bi-orthogonal relations for path-multiplicative solutions see Schmidt (1979, §2.2). …

24: 34 3j, 6j, 9j Symbols

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25: Bibliography I

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On polynomials orthogonal with respect to certain Sobolev inner products. J. Approx. Theory 65 (2), pp. 151–175.

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External Links:

ISSN 0021-9045, Document, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§18.36(ii).

Encodings:

BibTeX

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Two families of orthogonal polynomials related to Jacobi polynomials. Rocky Mountain J. Math. 21 (1), pp. 359–375.

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External Links:

ISSN 0035-7596, MathReview (Joaquin Bustoz), ZentralBlatt

Referenced by:

§18.30(i).

Encodings:

BibTeX

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An electrostatics model for zeros of general orthogonal polynomials. Pacific J. Math. 193 (2), pp. 355–369.

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External Links:

ISSN 0030-8730, FullText, MathReview (T. Erber), ZentralBlatt

Referenced by:

§18.39(v).

Encodings:

BibTeX

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More on electrostatic models for zeros of orthogonal polynomials. Numer. Funct. Anal. Optim. 21 (1-2), pp. 191–204.

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External Links:

ISSN 0163-0563, FullText, MathReview (M. E. Muldoon), ZentralBlatt

Referenced by:

§18.39(v).

Encodings:

BibTeX

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Classical and Quantum Orthogonal Polynomials in One Variable. Encyclopedia of Mathematics and its Applications, Vol. 98, Cambridge University Press, Cambridge.

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External Links:

ISBN 978-0-521-78201-2; 0-521-78201-5, MathReview Entry, ZentralBlatt

Referenced by:

§1.4(v), Profile Mourad E.H. Ismail, Erratum (V1.0.20) for Chapter 18 Orthogonal Polynomials.

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26: Vadim B. Kuznetsov

… ►Kuznetsov published papers on special functions and orthogonal polynomials, the quantum scattering method, integrable discrete many-body systems, separation of variables, Bäcklund transformation techniques, and integrability in classical and quantum mechanics. …

27: Gerhard Wolf

… ►Wolf has published papers on Mathieu functions, orthogonal polynomials, and Heun functions. …

28: Mourad E. H. Ismail

… ►Ismail has published numerous papers on special functions, orthogonal polynomials, approximation theory, combinatorics, asymptotics, and related topics. His well-known book Classical and Quantum Orthogonal Polynomials in One Variable was published by Cambridge University Press in 2005 and reprinted with corrections in paperback in Ismail (2009). …

29: 18.25 Wilson Class: Definitions

§18.25 Wilson Class: Definitions

… ►For the Wilson class OP’s $p_n(x)$ with $x=\lambda (y)$: if the $y$-orthogonality set is $\{0,1,\mathrm{\dots },N\}$, then the role of the differentiation operator $d/dx$ in the Jacobi, Laguerre, and Hermite cases is played by the operator ${\mathrm{\Delta }}_y$ followed by division by ${\mathrm{\Delta }}_y(\lambda (y))$, or by the operator ${\nabla }_y$ followed by division by ${\nabla }_y(\lambda (y))$. Alternatively if the $y$-orthogonality interval is $(0,\mathrm{\infty })$, then the role of $d/dx$ is played by the operator ${\delta }_y$ followed by division by ${\delta }_y(\lambda (y))$. … ►Under certain conditions on their parameters the orthogonality range for the Wilson polynomials and continuous dual Hahn polynomials is $(0,\mathrm{\infty })\cup S$, where $S$ is a specific finite set, e. … ►

§18.25(ii) Weights and Standardizations: Continuous Cases

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30: 18.7 Interrelations and Limit Relations

§18.7 Interrelations and Limit Relations

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§18.7(i) Linear Transformations

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Legendre, Ultraspherical, and Jacobi

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§18.7(ii) Quadratic Transformations

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§18.7(iii) Limit Relations

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