Degenerate Gauss hypergeometric functions
نویسنده
چکیده
Throughout the paper, we denote this equation by E(a, b, c). Since Kummer we know that in general there are 24 hypergeometric series which express solutions of E(a, b, c). The subject of this paper is Gauss hypergeometric functions when some or all of the numbers a, b, c, c − a, c − b, a − b, c − a − b are integers. We refer to these functions and to corresponding hypergeometric equations as degenerate. (Note that in [Erd53] and [AS64], a hypergeometric equation is called degenerate only when a, b, c− a or c− b are integers.) In a degenerate case, some of the 24 Kummer’s hypergeometric solutions are terminating or undefined, relations between them degenerate. The monodromy group of
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