Theory Of Hypergeometric Functions
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Theory of Hypergeometric Functions
Author | : Kazuhiko Aomoto |
Publisher | : Springer Science & Business Media |
Total Pages | : 327 |
Release | : 2011-05-21 |
Genre | : Mathematics |
ISBN | : 4431539387 |
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This book presents a geometric theory of complex analytic integrals representing hypergeometric functions of several variables. Starting from an integrand which is a product of powers of polynomials, integrals are explained, in an open affine space, as a pair of twisted de Rham cohomology and its dual over the coefficients of local system. It is shown that hypergeometric integrals generally satisfy a holonomic system of linear differential equations with respect to the coefficients of polynomials and also satisfy a holonomic system of linear difference equations with respect to the exponents. These are deduced from Grothendieck-Deligne’s rational de Rham cohomology on the one hand, and by multidimensional extension of Birkhoff’s classical theory on analytic difference equations on the other.
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