# Krätzel Function as a Function of Hypergeometric Type

Kilbas, Anatoly; Saxena, R. K.; Trujillo, Juan

Fractional Calculus and Applied Analysis (2006)

- Volume: 9, Issue: 2, page 109-131
- ISSN: 1311-0454

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topKilbas, 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 -

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