On some transformation formulas and their applications to partial theta function identities
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Abstract
In this paper we derive three new transformation formulae for bilateral basic hypergeometric series. As applications of these transformation formulae, we deduce the well-known q-Guass summation formula and Sear's two 3φ2 transformation formulae. Further, we establish the reciprocity theorem of Ramanujan and its three variable generalization.
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Vidya, K. N., & Somashekara, D. D. (2017). On some transformation formulas and their applications to partial theta function identities. Gulf Journal of Mathematics, 5(2). https://doi.org/10.56947/gjom.v5i2.95
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