# Basic Hypergeometric Series

@inproceedings{Gasper1990BasicHS, title={Basic Hypergeometric Series}, author={George Gasper and Mizan Rahman}, year={1990} }

Foreword Preface 1. Basic hypergeometric series 2. Summation, transformation, and expansion formulas 3. Additional summation, transformation, and expansion formulas 4. Basic contour integrals 5. Bilateral basic hypergeometric series 6. The Askey-Wilson q-beta integral and some associated formulas 7. Applications to orthogonal polynomials 8. Further applications 9. Linear and bilinear generating functions for basic orthogonal polynomials 10. q-series in two or more variables 11. Elliptic…

## 2,468 Citations

SUMMATION, TRANSFORMATION, AND EXPANSION FORMULAS FOR MULTIBASIC THETA HYPERGEOMETRIC SERIES

- Mathematics
- 2005

After reviewing some fundamental facts from the theory of theta hypergeometric series we derive, using indefinite summation, several summa- tion, transformation, and expansion formulas for multibasic…

Three-term relations for basic hypergeometric series

- MathematicsJournal of Mathematical Analysis and Applications
- 2018

Macdonald Polynomials and Multivariable Basic Hypergeometric Series

- Mathematics
- 2007

We study Macdonald polynomials from a basic hypergeometric series point of view. In particular, we show that the Pieri formula for Macdonald polynomials and its recently discovered inverse, a…

Summations for basic hypergeometric series involving a q-analogue of the digamma function

- Mathematics
- 1996

Transformation Formulas for Bilinear Sums of Basic Hypergeometric Series

- MathematicsCanadian Mathematical Bulletin
- 2016

Abstract A master formula of transformation formulas for bilinear sums of basic hypergeometric series is proposed. It is obtained from the author’s previous results on a transformation formula for…

Quadratic transformation formulas for basic hypergeometric series

- Mathematics
- 1993

Starting with some of the known transformation formulas for well-poised 2 φ 1 and very-well-poised 8 φ 7 basic hypergeometric series we obtain q-analogues of 36 quadratic transformation formulas…

On finite forms of certain bilateral basic hypergeometric series and their applications

- Mathematics
- 2016

In this paper we derive finite forms of the summation formulas for bilateral basic hypergeometric series 3 3, 4 4 and 5 5. We therefrom obtain the summation formulae obtained recently by Wenchang CHU…

BASIC HYPERGEOMETRIC FUNCTIONS AND ORTHOGONAL LAURENT POLYNOMIALS

- Mathematics
- 2012

A three-complex-parameter class of orthogonal Laurent polynomials on the unit circle associated with basic hypergeometric or q-hypergeometric functions is considered. To be precise, we consider the…

Transformation formulas for double hypergeometric series related to 9-j coefficients and their basic analogs

- Mathematics
- 2001

In a recent paper, Alisauskas deduced different triple sum expressions for the 9-j coefficient of su(2) and suq(2). For a singly stretched 9-j coefficient, these reduce to different double sum…

A quadratic formula for basic hypergeometric series related to Askey-Wilson polynomials

- Mathematics
- 2012

We prove a general quadratic formula for basic hypergeometric series, from which simple proofs of several recent determinant and Pfaffian formulas are obtained. A special case of the quadratic…