Operator factorization method and addition formulas for hypergeometric functions

DOI10.1080/10652460108819298zbMath0989.33006OpenAlexW1992220233MaRDI QIDQ2759212

A. W. Niukkanen

Publication date: 19 March 2002

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652460108819298

zbMATH Keywords

hypergeometric seriesJacobi polynomialsGegenbauer polynomialsBessel functionsduality theoremfactorization techniqueadditon formulasKoornwinder formula

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Generalized hypergeometric series, ({}_pF_q) (33C20) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Appell, Horn and Lauricella functions (33C65)

Cites Work

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• Extending the factorization principle to hypergeometric series of general form
• A transformation of \(F_4\) suggestive of a new approach to symbolic manipulation programming
• Some Polynomial Expansions for Functions of Several Variables
• SOME EXPANSIONS IN BESSEL FUNCTIONS INVOLVING APPELL'S FUNCTION F₄
• EXPANSIONS OF APPELL'S DOUBLE HYPER-GEOMETRIC FUNCTIONS (II)

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