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Certain integral transforms and fractional integral formulas for the extended hypergeometric functions. (English) Zbl 1376.44001

Summary: In this present paper, we derive various integral transforms, including Euler, Varma, Laplace, and Whittaker integral transforms for the extended hypergeometric functions which has recently been introduced by J. Choi et al. [Honam Math. J. 36, No. 2, 357–385 (2014; Zbl 1298.33004)]. Further, we also apply Saigo’s fractional integral operators for this extended hypergeometric function. Some interesting special cases of our main results are also considered.

MSC:

44A10 Laplace transform
33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals)
33B15 Gamma, beta and polygamma functions
33C05 Classical hypergeometric functions, \({}_2F_1\)
33C20 Generalized hypergeometric series, \({}_pF_q\)

Citations:

Zbl 1298.33004
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