Bessel functions of two variables as solutions for systems of the second order differential equations

Abstract

In this paper, the systems with solutions in the form of degenerate hypergeometric Humbert functions of two variables reduced to Bessel functions of two variables are established and studied. The connections between the Humbert and Bessel functions of two variables are revealed, their differential properties are investigated. The addition and multiplication theorems are proved. In future, these proven properties allow us to establish recurrent relations between degenerate hypergeometric functions of two variables, similarly to extend these properties to the case of many variables. The connection between type systems of Bessel and Whittaker is shown. Using the Frobenius-Latysheva method, the singularities of constructing normalregular solutions of the newly established Bessel-type system are studied.