Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

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**lanxiyu****Member**- Registered: 2022-05-10
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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:

Degenerate cases:

*Last edited by lanxiyu (2024-04-07 15:27:36)*

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