Ramanujan series with a shift

2018/02/06 by Jesús Guillera, Guillera, Jesús
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1802.02023

13 pages. Extended and improved version

arxiv created 2018/03/20 · arxiv updated 2018/03/21

Abstract

We consider an extension of the Ramanujan series with a variable x. If we let x=x₀, we call the resulting series: "Ramanujan series with the shift x₀". Then, we relate these shifted series to some q-series and solve the case of level 4 with the shift x₀=1/2. Finally, we indicate a possible way towards proving some patterns observed by the author corresponding to the levels ℓ=1, 2, 3 and the shift x₀=1/2.

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