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#1 2024-02-24 23:54:43

lanxiyu
Member
Registered: 2022-05-10
Posts: 64

Lemniscate functions

Notations:








Specific values:


















Differential equations:


























Pythagoras-like identities:





Opposite angle identities:








Double angle identities:







Triple angle identities:





Half angle identities:






Angle sum and difference identities:







Translation by real quarter-periods:






Translation by imaginary quarter-periods:






Translation by real half-periods:








Translation by imaginary half-periods:








Quarter-turn rotations:








Multiplied by (1±i):






Divided by (1±i):




Indefinite integrals:
































Definite integrals:


Inverse functions:



























Last edited by lanxiyu (2025-02-26 21:51:12)

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