# Math Is Fun Forum

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

You are not logged in.

## #1 2023-10-09 03:33:59

lanxiyu
Member
Registered: 2022-05-10
Posts: 50

### Jacobi elliptic functions identities

Notations:

Specific values:

Differential equations:

Pythagoras-like identities:

Opposite angle identities:

Double angle identities:

Half angle identities:

Angle sum and difference identities:

Translation by real quarter-period:

Translation by imaginary quarter-period:

Translation by real half-period:

Translation by imaginary half-period:

Jacobi imaginary transformations:

Jacobi real transformations:

Indefinite integrals:

Theta function representations:

Value of Jacobi amplitude:

Degenerate cases:

Conversion (q = nome, τ = half period ratio, α = modular angle, k = elliptic modulus, k' = complementary elliptic modulus, m = elliptic parameter):

Differential function solution:

Numerical computation of Jacobi elliptic functions
Notation for the theta functions

Last edited by lanxiyu (2024-06-30 18:40:26)

Offline