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- Title
On Transformation and Summation Formulas for Some Basic Hypergeometric Series.
- Authors
Somashekara, D. D.; Shalini, S. L.; Vidya, K. N.
- Abstract
In this paper, we give an alternate and simple proofs for Sear's three term 3ϕ2 transformation formula, Jackson's 3ϕ2 transformation formula and for a nonterminating form of the q-Saalschütz sum by using q-exponential operator techniques. We also give an alternate proof for a nonterminating form of the q-Vandermonde sum. We also obtain some interesting special cases of all the three identities, some of which are analogous to the identities stated by Ramanujan in his lost notebook.
- Subjects
HYPERGEOMETRIC distribution; Q-series; EXPONENTIAL functions; VANDERMONDE matrices; THETA functions
- Publication
International Journal of Mathematical Combinatorics, 2017, Vol 1, p22
- ISSN
1937-1055
- Publication type
Article