``The'' Jacobi identity is a relationship
Relationships between the Q-Function are also known as Jacobi identities:
See also Commutator, Jacobi Triple Product, Q-Function, Weber Functions
Borwein, J. M. and Borwein, P. B. Pi & the AGM: A Study in Analytic Number Theory and Computational Complexity.
New York: Wiley, 1987.