On approximation and computation of modified Bessel functions of complex order

Abstract

Easy-to-compute approximations of modified Bessel functions for any complex order are found. The case of two second-order differential equations with polynomial coefficients is considered. For approximately solving them, a scheme based on canonical vector-polynomials introduced by the author is proposed. The functions under consideration are of significant interest in light of the introduction of a new class of Yakubovich integral transforms.