{"product_id":"theory-of-hypergeometric-functions-9784431540878","title":"Theory of Hypergeometric Functions","description":"\u003cp\u003e • Author(s): Kazuhiko Aomoto\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Geometry - General\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis 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.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Paperback","offer_id":45282638692503,"sku":"9784431540878","price":6610.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9784431540878.webp?v=1769302735","url":"https:\/\/atlanticbooks.com\/products\/theory-of-hypergeometric-functions-9784431540878","provider":"Atlantic Books","version":"1.0","type":"link"}