Quintuple product identity - Alchetron, the free social encyclopedia

In mathematics the Watson quintuple product identity is an infinite product identity introduced by Watson (1929) and rediscovered by Bailey (1951) and Gordon (1961). It is analogous to the Jacobi triple product identity, and is the Macdonald identity for a certain non-reduced affine root system.

Statement

∏ n ≥ 1 ( 1 − s n ) ( 1 − s n t ) ( 1 − s n − 1 t − 1 ) ( 1 − s 2 n − 1 t 2 ) ( 1 − s 2 n − 1 t − 2 ) = ∑ n ∈ Z s ( 3 n 2 + n ) / 2 ( t 3 n − t − 3 n − 1 )

References

Quintuple product identity Wikipedia

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