Abstract
We study Andrews and Berndt’s organization of Ramanujan’s transformation formulas in Chapter 1 of their book Ramanujan’s Lost Notebook, Part II. In the process, we rediscover a bibasic Heine’s transformation, which follows from a Fundamental Lemma given by Andrews in 1966, and obtain identities proximal to Ramanujan’s entries. We also provide a multibasic generalization of Andrews’ 1972 theorem concerning a q-analog of the Lauricella function. Our results only require the q-binomial theorem, and are an application of what Andrews and Berndt call ‘Heine’s Method’.
Dedicated to Krishnaswami Alladi on his 60th birthday
Research supported in part by the Austrian Science Fund (FWF): F 5008-N15.
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Acknowledgements
We thank Professor George Andrews and Professor Christian Krattenthaler for many suggestions, pointers to useful references, and helpful discussions.
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Bhatnagar, G. (2017). A Bibasic Heine Transformation Formula and Ramanujan’s \(_2\phi _1\) Transformations. In: Andrews, G., Garvan, F. (eds) Analytic Number Theory, Modular Forms and q-Hypergeometric Series. ALLADI60 2016. Springer Proceedings in Mathematics & Statistics, vol 221. Springer, Cham. https://doi.org/10.1007/978-3-319-68376-8_8
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