Abstract
In this paper, we obtain new transformation and summation formulae for bilateral basic hypergeometric series and give a simple proof of Jacobi’s triple product identity. Further, we present applications of the main results.
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Acknowledgements
The authors are thankful to the referee for his valuable suggestions which has considerably improved the quality of the paper. The first author is thankful to University Grants Commission (UGC), India for financial support under the grant SAPDRS-1-NO.F.510/12/DRS-II/2018. The second author is thankful to UGC for awarding the Basic Science Research Fellowship, No. F.25-1/2014-15(BSR)/No. F.7-349/2012(BSR).
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Somashekara, D.D., Vidya, K.N. On transformation of certain bilateral basic hypergeometric series and their applications. Proc Math Sci 129, 44 (2019). https://doi.org/10.1007/s12044-019-0499-3
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DOI: https://doi.org/10.1007/s12044-019-0499-3
Keywords
- Bilateral basic hypergeometric series
- Jacobi’s triple product identity
- mock theta functions
- theta functions