Q theta function - Alchetron, The Free Social Encyclopedia

In mathematics, the q-theta function is a type of q-series. It is given by

θ ( z ; q ) = ∏ n = 0 ∞ ( 1 − q n z ) ( 1 − q n + 1 / z )

where one takes 0 ≤ |q| < 1. It obeys the identities

θ ( z ; q ) = θ ( q z ; q ) = − z θ ( 1 z ; q ) .

It may also be expressed as:

θ ( z ; q ) = ( z ; q ) ∞ ( q / z ; q ) ∞

where ( ⋅ ⋅ ) ∞ is the q-Pochhammer symbol.

References

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