Geodesic
Krätzel Function as a Function of Hypergeometric Type
Fractional calculus and applied analysis, Tome 9 (2006) no. 2, pp. 109-131.

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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.
Keywords: Krätzel Function, H-Function, Generalized Hypergeometric Wright Function, Generalized Hypergeometric Function, Mellin Transform, 33C60, 33C20, 44A15 
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     title = {Kr\"atzel {Function} as a {Function} of {Hypergeometric} {Type}},
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Kilbas, Anatoly; Saxena, R. K.; Trujillo, Juan. Krätzel Function as a Function of Hypergeometric Type. Fractional calculus and applied analysis, Tome 9 (2006) no. 2, pp. 109-131. http://geodesic.mathdoc.fr/item/FCAA_2006_9_2_a2/