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.
