Some Quadratic and Cubic Summation Formulas for Basic Hypergeometric Series
- 1 April 1993
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 45 (2) , 394-411
- https://doi.org/10.4153/cjm-1993-020-8
Abstract
An identity of L. Carlitz for a bibasic hypergeometric series is used to find some summation formulas for series in which the bases are either q and q2 or q and q3,0 < q < 1 In general, these series are neither balanced nor very-well-poised in the usual senseKeywords
This publication has 6 references indexed in Scilit:
- Positivity of the Poisson Kernel for the Continuous q-Jacobi Polynomials and Some Quadratic Transformation Formulas for Basic Hypergeometric SeriesSIAM Journal on Mathematical Analysis, 1986
- Another family of q-Lagrange inversion formulasRocky Mountain Journal of Mathematics, 1986
- On Quadratic Transformations of Basic SeriesSIAM Journal on Mathematical Analysis, 1984
- Strange Evaluations of Hypergeometric SeriesSIAM Journal on Mathematical Analysis, 1982
- Some inverse relationsDuke Mathematical Journal, 1973
- On the Transformation Theory of Basic Hypergeometric FunctionsProceedings of the London Mathematical Society, 1951