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

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

2011-08-25

arxiv.org/abs/1108.4980v2

Mathematics

Classical Analysis and ODEs

12 pages

Scientific paper

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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