In mathematics, a general hypergeometric function or Aomoto–Gelfand hypergeometric function is a generalization of the

hypergeometric function In mathematics, the Gaussian or ordinary hypergeometric function 2''F''1(''a'',''b'';''c'';''z'') is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting cases. It is ...

that was introduced by . The general hypergeometric function is a function that is (more or less) defined on a

Grassmannian In mathematics, the Grassmannian \mathbf_k(V) (named in honour of Hermann Grassmann) is a differentiable manifold that parameterizes the set of all k-dimension (vector space), dimensional linear subspaces of an n-dimensional vector space V over a ...

, and depends on a choice of some complex numbers and signs.

References

*{{Citation , last1=Gelfand , first1=I. M. , authorlink=Israel Gelfand , title=General theory of hypergeometric functions , mr=841131 , year=1986 , journal=Doklady Akademii Nauk SSSR , issn=0002-3264 , volume=288 , issue=1 , pages=14–18 (English translation in collected papers, volume III.) * Aomoto, K. (1975), "Les équations aux différences linéaires et les intégrales des fonctions multiformes", ''J. Fac. Sci. Univ. Tokyo, Sect. IA Math.'' 22, 271-229. Hypergeometric functions