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Basic Hypergeometric Series George Gasper

Book Details:

Author: George Gasper
Published Date: 20 Feb 2014
Publisher: CAMBRIDGE UNIVERSITY PRESS
Book Format: Book
ISBN10: 1306148634
Publication City/Country: United States
Filename: basic-hypergeometric-series.pdf

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Inversion techniques and combinatorial identities. Strange evaluations of basic hypergeometric series. Chu, Wenchang. Compositio Mathematica, Tome 91 series from the Jacobi theta functions that generalize the plain and basic hy-pergeometric series. Single and multivariable elliptic hypergeometric series are considered in detail. A characterization theorem for a single variable totally elliptic hypergeometric series is proved. Contents 1. Introduction 1 2. Theta hypergeometric series rE s and Askey, Richard. Review: Nathan J. Fine, Basic hypergeometric series and applications. Bull. Amer. Math. Soc. (N.S.) 21 (1989), no. 1, 130 -132. 79. Abstract. An incomplete survey of hypergeometric series is given, and some of. Ramanujan's work on hypergeometric and basic hypergeometric series is put. The subject of basic hypergeometric series has been developed to such an extent, with such a profusion of powerful and general results, expressed in so compact a notation, as to make it appear quite formidable to the neophyte. Nevertheless, the beauty and surprising nearness to 2.1 Definition. An general hypergeometric function is defined the serie A simple example of the value of Pochhammer's symbol is (1)k = 1* 2*.*k = k! Similarly, in the setting of truncated basic hypergeometric series, congruences modulo some power of a cyclotomic polynomial are special and, q-Stokes phenomenon on basic hypergeometric series. Yousuke Ohyama with Changgui Zhang (Lille). Tokushima University, Japan. 1.1 Introduction. 1.2 Hypergeometric and basic hypergeometric series. 1.3 The q-binomial theorem. 1.4 Heine's transformation formulas for 201 Basic hypergeometric functions are among the most important functions with very diverse applications to Engineering,Physics and Mathematical Analy- sis. 1.2 Basic Hypergeometric Theory. The hyperbolic hypergeometric functions are closely related to the much better known basic hypergeometric Moreover, I will prove that the basic hypergeometric functions rΦs are Keywords: Basic hypergeometric series, q-Difference operators, q-Difference equations. A hypergeometric series whose parameters are (a 1, b, c), (a, b 1, c) or. (a, b, c 1) is called contiguous to F(a, b, c; z). Gauss worked out the basic cases. In mathematics, the Gaussian or ordinary hypergeometric function 2F1(a,b;c;z) is a special function represented the hypergeometric series, that includes many other special functions as specific or limiting cases. It is a solution of a second-order linear ordinary differential equation (ODE). Every second-order linear ODE with three regular Elliptic Pochhammer symbol and hypergeometric series: |q|,|p| < 1. (a;p):= (a;p) (a 1p G. Gasper and M. Rahman, Basic hypergeometric series. 2nd edn. Abstract. In the lecture notes we start off with an introduction to the q-hypergeometric series, or basic hypergeometric series, and we derive Keywords and phrases: Basic hyper geometric series, Continued fractions and some known results in basic hyper geometric series. I. Definitions And Notations n (basic) hypergeometric series have also been referred to as SU(n) or U(n) series, the terminology (basic) hypergeometric series associated to the root system A n, or simply A n (basic) hypergeometric series, is preferred most authors nowadays. A further important development was Gustafson s introduction of very-well-poised series

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