Abstract
In this paper, we derive a new transformation formula for bilateral \(_6\psi _6\) series using Roger’s \(_6\phi _5\) summation and then use it to deduce the well-known Bailey’s \(_6\psi _6\) summation formula. Also, we deduce some identities involving theta functions and new identities analogous to identities of Ramanujan. Further, we give formulas for finding the number of representations of an integer as sums of squares and sums of triangular numbers.
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The authors would like to thank the referee for useful and constructive suggestions which considerably improved the quality of this paper.
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The first author was supported by the University Grants Commission (UGC), India, under the grant SAP-DRS-1 No.F.510/2/DRS/2011. The second author was supported by UGC, India, with the award of a Teacher Fellowship under the Grant No. KAMY074-TF01-13112010.
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Somashekara, D.D., Narasimha Murthy, K. On a new transformation formula for bilateral \(_6{\psi }_6\) series and applications. Ramanujan J 42, 1–13 (2017). https://doi.org/10.1007/s11139-016-9846-5
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DOI: https://doi.org/10.1007/s11139-016-9846-5