Theory of Hypergeometric Functions
Seiten
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.
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.
Reihe/Serie | Springer Monographs in Mathematics |
---|---|
Mitarbeit |
Anhang von: Toshitake Kohno |
Übersetzer | Kenji Iohara |
Zusatzinfo | XVI, 320 p. |
Verlagsort | Tokyo |
Sprache | englisch |
Maße | 155 x 235 mm |
Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
ISBN-10 | 4-431-53912-3 / 4431539123 |
ISBN-13 | 978-4-431-53912-4 / 9784431539124 |
Zustand | Neuware |
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Buch | Hardcover (2022)
Hanser, Carl (Verlag)
29,99 €