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RAMANUJAN SERIES WITH A SHIFT

Published online by Cambridge University Press:  23 October 2018

JESÚS GUILLERA*
Affiliation:
Department of Mathematics, University of Zaragoza, 50009 Zaragoza, Spain email [email protected]
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Abstract

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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
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

References

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