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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 $x_{0}=1/2$ .

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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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