TY - JOUR
T1 - Two-dimensional series evaluations via the elliptic functions of Ramanujan and Jacobi
AU - Berndt, Bruce C.
AU - Lamb, George
AU - Rogers, Mathew
N1 - Funding Information:
The research of Bruce C. Berndt was supported by National Security Agency grant H98230-11-1-0200. The research of Mathew Rogers was supported by National Science Foundation grant DMS-0803107.
PY - 2012/12
Y1 - 2012/12
N2 - 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.
AB - 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.
KW - Class invariants
KW - Cubic continued fraction
KW - Hypergeometric functions
KW - Jacobian elliptic functions
KW - Ramanujan's theta functions
KW - Rogers-Ramanujan continued fraction
KW - Singular moduli
KW - Two-dimensional lattice sums
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U2 - 10.1007/s11139-011-9351-9
DO - 10.1007/s11139-011-9351-9
M3 - Article
AN - SCOPUS:84869137485
SN - 1382-4090
VL - 29
SP - 185
EP - 198
JO - Ramanujan Journal
JF - Ramanujan Journal
IS - 1-3
ER -