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Generalized hypergeometric functions associated with an arbitrary finite or locally compact continuous field. (English. Russian original) Zbl 0801.33020
Russ. Acad. Sci., Dokl., Math. 45, No. 2, 343-347 (1992); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 323, No. 3, 394-397 (1992).
Notions of hypergeometric systems of differential equations and its solutions, hypergeometric functions are generalized from $$\mathbb{R}^ n$$ to $$F^ n$$, where $$F$$ is a finite or locally compact continuous field. Hypergeometric functions are defined as distributions on $$F^ n$$.
##### MSC:
 33C80 Connections of hypergeometric functions with groups and algebras, and related topics 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods 35D99 Generalized solutions to partial differential equations