Abstract
On page 310 of his second notebook, Ramanujan recorded two theta function identities. B. C. Berndt proved them by the method of parameterization. The purpose of this article is to give an elementary proof for those two identities and also we have obtained two theta function identities which are analogues to the identities of Ramanujan. Further, we establish two distinct formula for 3-core partitions in terms of divisor function.
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Acknowledgements
Authors would like to thank anonymous referee for their valuable comments and bringing our attention to [4,5,6, 8]. The first author is supported by grant Ref. No.:191620127010/(CSIR-UGC NET DEC.2019) by the funding agency University Grants Commission, Government of India under Joint CSIR-UGC JRF scheme. The author is grateful to funding agency.
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Communicated by Sanoli Gun.
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Vasuki, K.R., Shankar, A.I.V. On two theta function identities of Ramanujan. Indian J Pure Appl Math 54, 1099–1104 (2023). https://doi.org/10.1007/s13226-022-00323-9
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DOI: https://doi.org/10.1007/s13226-022-00323-9