Some generating relations for extended Appell's and Lauricella's hypergeometric functions

DOI10.1216/RMJ-2014-44-6-1987zbMath1308.33009MaRDI QIDQ2514552

Hong-Mei Liu

Publication date: 3 February 2015

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmjm/1422885104

zbMATH Keywords

beta functionKummer's functionAppell's hypergeometric functionsLauricella's hypergeometric function

Mathematics Subject Classification ID

Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Gamma, beta and polygamma functions (33B15) Integral transforms of special functions (44A20) Appell, Horn and Lauricella functions (33C65) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15)

Related Items

Certain integral transform and fractional integral formulas for the generalized Gauss hypergeometric functions, Extension of Exton’s hypergeometric function K16

Cites Work

• Unnamed Item
• Unnamed Item
• Extension of gamma, beta and hypergeometric functions
• Some generating relations for extended hypergeometric functions via generalized fractional derivative operator
• Mellin transforms and asymptotics: Harmonic sums
• Extension of Euler's beta function
• Extended hypergeometric and confluent hypergeometric functions
• Recursion formulas for Appell's hypergeometric function \(F_2\) with some applications to radiation field problems
• Specialization of Appell's functions to univariate hypergeometric functions
• Some reduction and transformation formulas for the Appell hypergeometric function \(F_{2}\)
• Summation formulas associated with the Lauricella function \(F_A^{(\tau)}\)
• Decomposition formulas associated with the Lauricella multivariable hypergeometric functions
• Some decomposition formulas associated with the Lauricella function \(F_{A}^{(r)}\) and other multiple hypergeometric functions