نتایج جستجو برای: gauss hypergeometric function

تعداد نتایج: 1224797  

2003
Raimundas Vidūnas

A celebrated theorem of Klein implies that any hypergeometric differential equation with algebraic solutions is a pull-back of one of the few standard hypergeometric equations with algebraic solutions. The most interesting cases are hypergeometric equations with tetrahedral, octahedral or icosahedral monodromy groups. We give an algorithm for computing Klein’s pull-back coverings in these cases...

2008
Robert S. Maier

A unified treatment is given of low-weight modular forms on Γ0(N), N = 2, 3, 4, that have Eisenstein series representations. For each N, certain weight-1 forms are shown to satisfy a coupled system of nonlinear differential equations, from which a single nonlinear third-order equation, called a generalized Chazy equation, can be derived. As byproducts of this result, a table of divisor function...

Journal: :Publications of the Research Institute for Mathematical Sciences 2019

2007
Julien Roques

In this paper we compute the Galois groups of basic hypergeometric equations. In this paper q is a complex number such that 0 < |q| < 1. 1 Basic hypergeometric series and equations The theory of hypergeometric functions and equations dates back at least as far as Gauss. It has long been and is still an integral part of the mathematical literature. In particular, the Galois theory of (generalize...

2002
P. J. Forrester

Application of the τ-function theory of Painlevé equations to random matrices: Okamoto has obtained a sequence of τ-functions for the PVI system expressed as a double Wron-skian determinant based on a solution of the Gauss hypergeometric equation. Starting with integral solutions of the Gauss hypergeometric equation, we show that the determinant can be re-expressed as multi-dimensional integral...

Journal: :Applied Mathematics & Information Sciences 2014

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