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Contiguity relations of generalized confluent hypergeometric functions. (English) Zbl 0812.33007
Generalized confluent hypergeometric systems were formulated in the earlier papers of I. M. Gel’fand, V. S. Retakh and V. V. Serganova [Sov. Math. Dokl. 37, No. 1, 8-12 (1988); translation from Dokl. Akad. Nauk SSSR 298, No. 1, 17-21 (1988; Zbl 0699.33012)] and of H. Kimura, Y. Haraoka and K. Takano [Proc. Jap. Acad., Ser. A 68, 290-295 (1992; Zbl 0773.33004)]. This paper shows how to get contiguity operators between two such systems with distinct parameters differing by integers and proves that the set of such operators has a Lie algebra structure. This generalizes a result of the reviewer [SIAM J. Math. Anal. 22, No. 3, 821-846 (1991; Zbl 0805.33003)]. Note that each of such operators gives a contiguity relation among the confluent hypergeometric functions and that the Lie algebra as a whole explains the symmetry of the system.
Reviewer: T.Sasaki (Kobe)

MSC:
33C70 Other hypergeometric functions and integrals in several variables
33C15 Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\)
33C80 Connections of hypergeometric functions with groups and algebras, and related topics
17B66 Lie algebras of vector fields and related (super) algebras
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