Two-dimensional series evaluations via the elliptic functions of Ramanujan and Jacobi
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- Berndt, B.C., Lamb, G. & Rogers, M. Ramanujan J (2012) 29: 185. doi:10.1007/s11139-011-9351-9
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.
KeywordsTwo-dimensional lattice sums Ramanujan’s theta functions Class invariants Singular moduli Rogers-Ramanujan continued fraction Cubic continued fraction Jacobian elliptic functions Hypergeometric functions
Mathematics Subject Classification (2000)33E05 11F03 11F27
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