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arXiv · 1908.09596

On a new parameter involving Ramanujan's theta-functions

S. Chandankumar·H. S. Sumanth Bharadwaj·Vijay Yadav
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Abstract

We define a new parameter $A'_{k,n}$ involving Ramanujan's theta-functions for any positive real numbers $k$ and $n$ which is analogous to the parameter $A_{k,n}$ defined by Nipen Saikia \cite{NS1}. We establish some modular relation involving $A'_{k,n}$ and $A_{k,n}$ to find some explicit values of $A'_{k,n}$. We use these parameters to establish few general theorems for explicit evaluations of ratios of theta functions involving $\varphi(q)$.

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S. Chandankumar, H. S. Sumanth Bharadwaj, Vijay Yadav. 2019-08-26. On a new parameter involving Ramanujan's theta-functions. https://doi.org/10.56827/seajmms.2023.1902.3

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