Kilbas, Anatoly,
Saxena, R. K.,
Trujillo, Juan
(2006)
2000 Mathematics Subject Classification: 33C60, 33C20, 44A15
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...