On the Generalized Confluent Hypergeometric Function and Its Application

Virchenko, Nina

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HYPERG: a Maple package for manipulating hypergeometric series.

Gauthier, Bruno (1999)

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HYP and HYPQ. Mathematica packages for the manipulation of binomial sums and hypergeometric series respectively $q$ -binomial sums and basic hypergeometric series.

Krattenthaler, C. (1993)

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Masuda, Tetsu (2009)

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Kilbas, Anatoly, Saxena, R. K., Trujillo, Juan (2006)

Fractional Calculus and Applied Analysis

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2000 Mathematics Subject Classification: 33C60, 33C20, 44A15 The paper is devoted to the study of the function Zνρ(x) defined for positive x > 0, real ρ ∈ R and complex ν ∈ C, being such that Re(ν) < 0 for ρ ≤ 0, [...] Such a function was earlier investigated for ρ > 0. Using the Mellin transform of Zνρ(x), we establish its representations in terms of the H-function and extend this function from positive x > 0 to complex z. The results obtained, being different...