Krätzel Function as a Function of Hypergeometric Type
Fractional calculus and applied analysis, Tome 9 (2006) no. 2, pp. 109-131
Cet article a éte moissonné depuis la source Bulgarian Digital Mathematics Library
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
@article{FCAA_2006_9_2_a2,
author = {Kilbas, Anatoly and Saxena, R. K. and Trujillo, Juan},
title = {Kr\"atzel {Function} as a {Function} of {Hypergeometric} {Type}},
journal = {Fractional calculus and applied analysis},
pages = {109--131},
year = {2006},
volume = {9},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/FCAA_2006_9_2_a2/}
}
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 SP - 109 EP - 131 VL - 9 IS - 2 UR - http://geodesic.mathdoc.fr/item/FCAA_2006_9_2_a2/ LA - en ID - FCAA_2006_9_2_a2 ER -
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/