Krätzel Function as a Function of Hypergeometric Type

Kilbas, Anatoly, Saxena, R. K., and Trujillo, Juan. "Krätzel Function as a Function of Hypergeometric Type." Fractional Calculus and Applied Analysis 9.2 (2006): 109-131. <http://eudml.org/doc/11262>.

@article{Kilbas2006,
abstract = {2000 Mathematics Subject Classification: 33C60, 33C20, 44A15The 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.},
author = {Kilbas, Anatoly, Saxena, R. K., Trujillo, Juan},
journal = {Fractional Calculus and Applied Analysis},
keywords = {33C60; 33C20; 44A15},
language = {eng},
number = {2},
pages = {109-131},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Krätzel Function as a Function of Hypergeometric Type},
url = {http://eudml.org/doc/11262},
volume = {9},
year = {2006},
}

TY - JOUR
AU - Kilbas, Anatoly
AU - Saxena, R. K.
AU - Trujillo, Juan
TI - Krätzel Function as a Function of Hypergeometric Type
JO - Fractional Calculus and Applied Analysis
PY - 2006
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 9
IS - 2
SP - 109
EP - 131
AB - 2000 Mathematics Subject Classification: 33C60, 33C20, 44A15The 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.
LA - eng
KW - 33C60; 33C20; 44A15
UR - http://eudml.org/doc/11262
ER -