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Finite and infinite integral formulas involving the family of incomplete H-functions. (English) Zbl 1447.33008

Summary: Recent research focuses on the integral representations of the various type of special functions due to their potential applicability in different disciplines. In this line, we deal with several finite and infinite integrals involving the family of incomplete H-functions. Further, we point out some known and new special cases of these integrals. Finally, we establish the integral representation of incomplete H-functions.

MSC:

33C60 Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions)
33B15 Gamma, beta and polygamma functions
33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\)
33D70 Other basic hypergeometric functions and integrals in several variables
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