The Kratzel function and evaluation of integrals
This paper is devoted to the study of the special function Z(rho)(nu) (z) of z is an element of C with two parameters rho is an element of R and nu is an element of C. In a special case such a function coincides with the McDonald function. Using the representations of Z(rho)(nu)(z) in terms of the H-function, being different for rho > 0 and rho < 0, we deduce the asymptotic behavior of this function at zero and infinity and give applications to evaluation of integrals involving product of Z(rho)(nu)(x) and the H- and Meijer G-function, the Bessel function of the first kind, the McDonald function and cosine and sine functions. (C) 2009 Elsevier Ltd. All rights reserved.
kratzel function evaluation of integrals bessel functions cosine and sine functions h-function asymptotic estimates meijer g-function