Ramanujan series with a shift

Jesús Guillera

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arXiv · 1802.02023

Ramanujan series with a shift

Jesús Guillera

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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 $x_0=1/2$.

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Jesús Guillera. 2018-02-06. Ramanujan series with a shift. https://arxiv.org/abs/1802.02023

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