"The" Jacobi identity is a relationship
between three elements A, B, and C, where [A, B] is the commutator. The elements of a Lie algebra satisfy this identity.
Relationships between the Q-functions
are also known as Jacobi identities:
equivalent to the Jacobi triple product (Borwein and Borwein 1987, p. 65) and
where
is the complete elliptic integral of the first kind, and 
. Using Weber functions
(5) and (6) become
(Borwein and Borwein 1987, p. 69).
(1)
between three elements A, B, and C, where [A, B] is the commutator. The elements of a Lie algebra satisfy this identity.
Relationships between the Q-functions
are also known as Jacobi identities: (2)
equivalent to the Jacobi triple product (Borwein and Borwein 1987, p. 65) and
(3)
where
(4)
is the complete elliptic integral of the first kind, and . Using Weber functions(5)
(6)
(7)
(5) and (6) become
(8)
(9)
(Borwein and Borwein 1987, p. 69).
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