Theory of Hypergeometric Functions

This book presents a geometric theory of complex analytic integrals representing hypergeometric functions of several variables. It shows that hypergeometric integrals generally satisfy holonomic system of linear differential equations.

Inhaltsverzeichnis

1 Introduction: the Euler-Gauss Hypergeometric Function.- 2 Representation of Complex Integrals and Twisted de Rham Cohomologies.- 3 Hypergeometric functions over Grassmannians.- 4 Holonomic Difference Equations and Asymptotic Expansion References Index.

Zusammenfassung

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.

Produktdetails

• Autoren: Kazuhik Aomoto, Kazuhiko Aomoto, Michitake Kita
• Mitarbeit: Kenji Iohara (Übersetzung)
• Verlag: Springer, Berlin
• Originaltitel: Chokikakansuron
• Sprache: Englisch
• Produktform: Fester Einband
• Erschienen: 27.12.2010
• EAN: 9784431539124
• ISBN: 978-4-431-53912-4
• Seiten: 320
• Abmessung: 160 mm x 247 mm x 25 mm
• Gewicht: 630 g
• Illustration: XVI, 320 p.
• Serien: Springer Monographs in Mathematics; Schriftenreihe Markt und Marketing; Springer Monographs in Mathematics; Schriftenreihe Markt und Marketing
• Themen: Naturwissenschaften, Medizin, Informatik, Technik > Mathematik > Geometrie; B, Funktionalanalysis und Abwandlungen, geometry, Mathematics and Statistics, Functional Analysis, Functional analysis & transforms