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#1 2024-01-01 20:34:25

lanxiyu
Member
Registered: 2022-05-10
Posts: 39

General form of Dixon elliptic functions

Specific values:

With Λ=nλ(α)+n'λ'(α)+n''λ''(α):

Differential equations:

Integrals:

Identities:

Hypergeometric series representation:

Limit on branch cut:

Opposite angle formula:

Periodicity: with Λ=nλ(α)+n'λ'(α)+n''λ''(α):

Translation by one-third periods:

Addition theorems:

Double angle formulas:

Transformations:

Legendre's relation:

Weierstrass elliptic function representations:

Dedekind eta function representations:

Degenerate cases:

See On the doubly periodic functions arising out of the curve x³+y³-3αxy=1

Last edited by lanxiyu (2024-04-10 07:49:39)

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#2 2024-03-21 00:30:43

lanxiyu
Member
Registered: 2022-05-10
Posts: 39

Re: General form of Dixon elliptic functions

Specific values for α=0 case:

Last edited by lanxiyu (2024-03-22 02:35:12)

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