Abstract
In this paper, motivated by certain recent extensions of the Euler’s beta, Gauss’ hypergeometric and confluent hypergeometric functions (see [4]), we extend the Srivastava’s triple hypergeometric function H A by making use of two additional parameters in the integrand. Systematic investigation of its properties including, among others, various integral representations of Euler and Laplace type, Mellin transforms, Laguerre polynomial representation, transformation formulas and a recurrence relation, is presented. Also, by virtue of Luke’s bounds for hypergeometric functions and various bounds upon the Bessel functions appearing in the kernels of the newly established integral representations, we deduce a set of bounding inequalities for the extended Srivastava’s triple hypergeometric function H A,p,q .
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The research of T. K. Pogány has been supported in part by Croatian Science Foundation under the project No. 5435.
Original Russian Text © R. K. Parmar, T. K. Pogány, 2017, published in Izvestiya Natsional’noi Akademii Nauk Armenii, Matematika, 2017, No. 6, pp. 47-61.
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Parmar, R.K., Pogány, T.K. Extended Srivastava’s triple hypergeometric H A,p,q function and related bounding inequalities. J. Contemp. Mathemat. Anal. 52, 276–287 (2017). https://doi.org/10.3103/S1068362317060036
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DOI: https://doi.org/10.3103/S1068362317060036