Mathematics Subject Classification: 26A33, 33E12, 33C20. It has been shown that the fractional integration and differentiation operators transform such functions with power multipliers into the functions of the same form. Some of the results given earlier by Kilbas and Saigo follow as special cases.
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 for ρ >...
In this paper, we introduce certain multidimensional generalized Kober operators associated with the Gauss's hypergeometric function, which provide an elegant multivariate analogue of the operators introduced by Saxena and Kumbhat.
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