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General 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 is a space that parameterizes all -Dimension, dimensional linear subspaces of the -dimensional vector space . For example, the Grassmannian is the space of lines through the origin in , so it is the same as the ..., 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 fonct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grassmannian
In mathematics, the Grassmannian is a space that parameterizes all -Dimension, dimensional linear subspaces of the -dimensional vector space . For example, the Grassmannian is the space of lines through the origin in , so it is the same as the projective space of one dimension lower than . When is a real or complex vector space, Grassmannians are compact space, compact smooth manifolds. In general they have the structure of a smooth algebraic variety, of dimension k(n-k). The earliest work on a non-trivial Grassmannian is due to Julius Plücker, who studied the set of projective lines in projective 3-space, equivalent to and parameterized them by what are now called Plücker coordinates. Hermann Grassmann later introduced the concept in general. Notations for the Grassmannian vary between authors; notations include , , , or to denote the Grassmannian of -dimensional subspaces of an -dimensional vector space . Motivation By giving a collection of subspaces of some vecto ... [...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, ja, 日本数学会) 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 ... 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] |