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Title: Krätzel Function as a Function of Hypergeometric Type
Authors: Kilbas, Anatoly
Saxena, R. K.
Trujillo, Juan
Keywords: Krätzel Function
Generalized Hypergeometric Wright Function
Generalized Hypergeometric Function
Mellin Transform
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.
Description: 2000 Mathematics Subject Classification: 33C60, 33C20, 44A15
ISSN: 1311-0454
Appears in Collections:2006

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