“Jacobi Identities”的概念、定义、习题解题方法及翻译-数学辞典

单词

Jacobi Identities

释义

Jacobi Identities

``The'' Jacobi identity is a relationship

(1)

between three elements

, and

, where

is the Commutator. The elements of a Lie Groupsatisfy 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 WeberFunctions

(5) and (6) become

(8)

(9)

(Borwein and Borwein 1987, p. 69).

See also Commutator, Jacobi Triple Product, Q-Function, Weber Functions

References

Borwein, J. M. and Borwein, P. B. Pi & the AGM: A Study in Analytic Number Theory and Computational Complexity. New York: Wiley, 1987.

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