Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/1275

 Title: Krätzel Function as a Function of Hypergeometric Type Authors: Kilbas, AnatolySaxena, R. K.Trujillo, Juan Keywords: Krätzel FunctionH-FunctionGeneralized Hypergeometric Wright FunctionGeneralized Hypergeometric FunctionMellin Transform33C6033C2044A15 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 URI: http://hdl.handle.net/10525/1275 ISSN: 1311-0454 Appears in Collections: 2006

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