## Jacobi Identities

The'' Jacobi identity is a relationship

 (1)

between three elements , , and , where is the Commutator. The elements of a Lie Group satisfy this identity.

Relationships between the Q-Function 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).