RAMANUJAN SERIES WITH A SHIFT.

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 $x_{0}=1/2$. [ABSTRACT FROM AUTHOR]