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Definitions:
Conditions:
Parity:
Periodicity:
Homogeneity:
Transformation of half-periods :
Power series representations:
Recurrence relations of Eisenstein series:
Differential equations:
Integrals:
For definite integral, see https://www.mathisfunforum.com/viewtopic.php?id=30259
Values at lattice points:
Half period values:
One-third period values:
Quarter period values:
Translation by half-periods:
Translation by quarter-periods:
Addition theorems:
Triple addition formulas:
Double angle formulas:
Triple angle formulas:
Multiple angle formulas:
Half-angle formulas:
Quadratic transformations:
Relations involving squares:
Relations involving cubes:
Relations involving quartic powers:
Relations involving roots:
Sigma function representations:
Inverse functions:
Relations to Carlson elliptic integrals:
(see https://fungrim.org/topic/Carlson_symme … integrals/)
Relations to Jacobi elliptic functions:
Legendre's relation:
Lemniscatic cases:
Equianharmonic cases:
Degenerate cases:
Last edited by lanxiyu (2024-11-28 11:49:33)
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