Equations of hypergeometric type in the degenerate case

2017/04/23 by Dereziński, Jan, Karczmarczyk, Maciej
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1704.06981

Abstract

We consider the three most important equations of hypergeometric type, ₂F₁, ₁F₁ and ₁F₀, 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.

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