Fractional integral and generalized Stieltjes transforms for hypergeometric functions as transmutation operators

DOI10.3842/SIGMA.2015.074zbMath1325.33003arXiv1504.08144MaRDI QIDQ887754

Koornwinder, Tom H.

Publication date: 27 October 2015

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.08144

zbMATH Keywords

Stieltjes transformGauss hypergeometric functiontransmutation formulaEuler integral representationfractional integral transform

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Fractional derivatives and integrals (26A33) Integral transforms of special functions (44A20) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (6)

Generalized Stieltjes transforms of compactly-supported probability distributions: further examples ⋮ On a generalization of the Rogers generating function ⋮ First order linear differential equations with involutive delay and hypergeometric functions ⋮ Representations of hypergeometric functions for arbitrary parameter values and their use ⋮ From conformal group to symmetries of hypergeometric type equations ⋮ INTEGRAL REPRESENTATIONS FOR HORN'S <i>H</i>₂ FUNCTION AND OLSSON'S <i>F_P</i> FUNCTION

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