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RAMANUJAN SERIES WITH A SHIFT
Published online by Cambridge University Press: 23 October 2018
Abstract
We consider an extension of the Ramanujan series with a variable $x$. If we let $x=x_{0}$, we call the resulting series ‘Ramanujan series with the shift $x_{0}$’. Then we relate these shifted series to some $q$-series and solve the case of level $4$ with the shift $x_{0}=1/2$. Finally, we indicate a possible way towards proving some patterns observed by the author corresponding to the levels $\ell =1,2,3$ and the shift $x_{0}=1/2$.
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 107 , Issue 3 , December 2019 , pp. 367 - 380
- Copyright
- © 2018 Australian Mathematical Publishing Association Inc.