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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Theory of Hypergeometric Functions

Theory of Hypergeometric Functions

Aomoto, Kazuhiko
Kita, Michitake
Kohno, Toshitake

Paperback

Series: Springer Monographs in Mathematics

CalculusGeneral MathematicsGeometry

ISBN10: 4431540873
ISBN13: 9784431540878
Publisher: Springer Nature
Published: Jul 15 2013
Pages: 320
Weight: 1.06
Height: 0.69 Width: 6.16 Depth: 9.19
Language: English
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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