Theory of Hypergeometric Functions (eBook)

Kazuhiko Aomoto, Michitake Kita (Autoren)

eBook Download: PDF

2011 | 1. Auflage
320 Seiten
Springer-Verlag
9784431539384 (ISBN)

Infos

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.

Inhalt

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.

Produkt-Details

• Erscheint lt. Verlag: 21.5.2011
• Reihe/Serie: Springer Monographs in Mathematics
• Reihe/Serie: Springer Monographs in Mathematics
• Mitarbeit: Anhang von: Toshitake Kohno
• Übersetzer: Kenji Iohara
• Zusatzinfo: XVI, 320 p.
• Verlagsort: Tokyo
• Sprache: englisch
• Original-Titel: Chokikakansuron
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Technik
• Schlagworte: asymptotic behavior • Holonomic system of difference equations • Holonomic system of differential equations • Hypergeomtric function • Twisted de Rham cohomology
• ISBN-13: 9784431539384 / 9784431539384