engleski

Extended Srivastava's triple hypergeometric H_{;;A, p, q};; function and related bounding inequalities

Motivated by certain recent extensions of the Euler's beta, Gauss's hypergeometric and confluent hypergeometric functions [4], we extend Srivastava's triple hypergeometric function $H_{; ; ; A}; ; ; $ by making use of two additional parameters in the integrand. Systematic investigation of its properties, among others various integral representations of Euler and Laplace type, Mellin transforms, Laguerre polynomial representation, transformation formulae and a recurrence relation follow. 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}; ; ; $.

$(p ; q)$-extended Beta function ; $(p ; q)$-extended hypergeometric function ; Extended Appell function ; Mellin transforms ; ; Laguerre polynomial ; Recurrence relation ; Bounding inequality ; Luke's bounds for hypergeometric functions

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