INTEGRAL REPRESENTATIONS OF EULER-TYPE FOR THE QUADRUPLE HYPERGEOMETRIC FUNCTIONS $F^{(4)}_{20}$
Print ISSN: 2319-1023 | Online ISSN: 2582-5461 | Total Downloads : 141
DOI:
Author :
M. P. Chaudhary (Department of Mathematics Netaji Subhas University of Technology Sector 3, Dwarka, New Delhi 110078, INDIA)
Jihad A. Younis (Department of Mathematics University of Aden, Aden, YEMEN)
Abstract
The authors establish a set of fifteen new integral representations of Euler-type for the Sharma and Parihar hypergeometric function in four variables $F^{(4)}_{20}$; whose kernels include the quadruple functions $K_{1}, K_{10}, F^{(4)}_{14}$ and $X^{(4)}_{8}$; the Exton hypergeometric functions of three variables $X_{4}$; the Lauricella functions of three variable $F_{E}, F_{N}$ and $F_{R}$; the Appell’s series of two variables $F_{2}, F_{3}$ and $F_{4}$; and the Gauss hypergeometric function.
Keywords and Phrases
Beta function, Eulerian integrals, Quadruple hypergeometric series.
A.M.S. subject classification
33C20, 33C65.
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