Krätzel Function H-Function Generalized Hypergeometric Wright Function Generalized Hypergeometric Function Mellin Transform 33C60 33C20 44A15
Issue Date:
2006
Publisher:
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Fractional Calculus and Applied Analysis, Vol. 9, No 2, (2006), 109p-131p
Abstract:
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 > 0 and ρ < 0, are applied to obtain the explicit
forms of Zνρ(z) in terms of the generalized Wright function. The cases,
when such representations are expressed via the generalized hypergeometric
functions, are given.
