Some reduction and transformation formulas for the Appell hypergeometric function \(F_{2}\)

DOI10.1016/j.jmaa.2004.07.052zbMath1066.33013OpenAlexW2087158834MaRDI QIDQ1763410

Sheldon B. Opps, Nasser Saad, Hari M. Srivastava

Publication date: 22 February 2005

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2004.07.052

zbMATH Keywords

multiple hypergeometric functionsAppell series, hypergeometric series

Mathematics Subject Classification ID

Appell, Horn and Lauricella functions (33C65)

Related Items (16)

Reduction and transformation formulas for the Appell and related functions in two variables ⋮ On decomposition formulas related to the Gaussian hypergeometric functions in three variables ⋮ On certain new formulas for the Horn's hypergeometric functions \(\mathcal{G}_1\), \(\mathcal{G}_2\) and \(\mathcal{G}_3\) ⋮ Decomposition formulas for some triple hypergeometric functions ⋮ The second Appell function for one large variable ⋮ On the evaluation of the Appell \(F_2\) double hypergeometric function ⋮ \texttt{MultiHypExp}: a \textsc{Mathematica} package for expanding multivariate hypergeometric functions in terms of multiple polylogarithms ⋮ New formulas of the Bergman kernels for complex ellipsoids in $\mathbb {C}^2$ ⋮ A massive Feynman integral and some reduction relations for Appell functions ⋮ Decomposition formulas associated with the Lauricella multivariable hypergeometric functions ⋮ Unnamed Item ⋮ Some decomposition formulas associated with the Lauricella function \(F_{A}^{(r)}\) and other multiple hypergeometric functions ⋮ Applications of the operator \(H(\alpha ,\beta )\) to the Humbert double hypergeometric functions ⋮ Some generating relations for extended Appell's and Lauricella's hypergeometric functions ⋮ Recursion formulas for Appell's hypergeometric function \(F_2\) with some applications to radiation field problems ⋮ Unnamed Item

Cites Work

• A finite sum representation of the Appell series \(F_1 (a, b, b^{\prime}; c; x, y)\)
• Remarks on some associated Laguerre integral results
• Integrals of two confluent hypergeometric functions
• Integrals containing confluent hypergeometric functions with applications to perturbed singular potentials
• Some Integrals of the products of laguerre polynomials
• W. Gordon’s integral (1929) and its representations by means of Appell’s functions F2, F1, and F3
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