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Aomoto–Gel'fand Hypergeometric Function
In mathematics, a general hypergeometric function or Aomoto–Gelfand hypergeometric function is a generalization of the hypergeometric function 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 foncti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 a solution of a second-order linear ordinary differential equation (ODE). Every second-order linear ODE with three regular singular points can be transformed into this equation. For systematic lists of some of the many thousands of published identities involving the hypergeometric function, see the reference works by and . There is no known system for organizing all of the identities; indeed, there is no known algorithm that can generate all identities; a number of different algorithms are known that generate different series of identities. The theory of the algorithmic discovery of identities remains an active research topic. History The term "hypergeometric series" was first used by John Wallis in his 1655 book ''Arithmetica Infinitor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 field (mathematics), field K that has a differentiable structure. For example, the Grassmannian \mathbf_1(V) is the space of lines through the origin in V, so it is the same as the projective space \mathbf(V) of one dimension lower than V. When V is a real number, real or complex number, complex vector space, Grassmannians are compact space, compact smooth manifolds, of dimension k(n-k). In general they have the structure of a nonsingular projective algebraic variety. The earliest work on a non-trivial Grassmannian is due to Julius Plücker, who studied the set of projective lines in real projective 3-space, which is equivalent to \mathbf_2(\mathbf^4), parameterizing them by what are now called Plücker coordinates. (See below.) Herma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kazuhiko Aomoto
Kazuhiko Aomoto is a Japanese mathematician who introduced the Aomoto-Gel'fand hypergeometric function and the Aomoto integral. He was a professor at Nagoya University. In 1996 he received the Mathematical Society of Japan The Mathematical Society of Japan (MSJ, ) is a learned society for mathematics in Japan. In 1877, the organization was established as the ''Tokyo Sugaku Kaisha'' and was the first academic society in Japan. It was re-organized and re-established i ... autumn prize for his research on complex integration. References * 21st-century Japanese mathematicians Living people Year of birth missing (living people) Academic staff of Nagoya University Complex analysts {{Japan-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |