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 de...