The Krätzel function and evaluation of integrals

Evaluation of integrals Meijer G-function Bessel functions Cosine and sine functions a b s t r a c t This paper is devoted to the study of the special function Z ν ρ (z) of z ∈ C with two parameters ρ ∈ R and ν ∈ C. In a special case such a function coincides with the McDonald function. Using the representations of Z ν ρ (z) in terms of the H-function, being different for ρ > 0 and ρ < 0, we deduce the asymptotic behavior of this function at zero and infinity and give applications to evaluation of integrals involving product of Z ν ρ (x) and the Hand Meijer G-function, the Bessel function of the first kind, the McDonald function and cosine and sine functions.