Equations of hypergeometric type in the degenerate case

Abstract

We consider the three most important equations of hypergeometric type, ${}_2{F}_1$, ${}_1{F}_1$ and ${}_1{F}_0$, in the so-called degenerate case. In this case one of the parameters, usually denoted $c$, is an integer and the standard basis of solutions consists of a hypergeometric-type function and a function with a logarithmic singularity. This article is devoted to a thorough analysis of the latter solution to all three equations.