Two-dimensional series evaluations via the elliptic functions of Ramanujan and Jacobi

2011/08/25 by Bruce C. Berndt, Berndt, Bruce C., George Lamb +3
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT) #math.CA #math.NT

paper · pdf · doi:10.48550/arxiv.1108.4980

12 pages

arxiv created 2011/08/26 · arxiv updated 2011/08/29

Abstract

We evaluate in closed form, for the first time, certain classes of double series, which are remindful of lattice sums. Elliptic functions, singular moduli, class invariants, and the Rogers--Ramanujan continued fraction play central roles in our evaluations

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