Difference between revisions of "Q-theta function"
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(Created page with "For $0 \leq |q| < 1$, $$\theta(z;q)=\prod_{k=0}^{\infty} (1-q^kz) \left(1-\dfrac{q^{k+1}}{z} \right)=(z;q)_{\infty}(\frac{q}{z};q)_{\infty},$$ where $(a,b)_{\infty}$ is the...") |
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For $0 \leq |q| < 1$, | For $0 \leq |q| < 1$, | ||
| − | $$\theta(z;q)=\prod_{k=0}^{\infty} (1-q^kz) \left(1-\dfrac{q^{k+1}}{z} \right)=(z;q)_{\infty}(\frac{q}{z};q)_{\infty},$$ | + | $$\theta(z;q)=\prod_{k=0}^{\infty} (1-q^kz) \left(1-\dfrac{q^{k+1}}{z} \right)=(z;q)_{\infty}\left(\frac{q}{z};q \right)_{\infty},$$ |
where $(a,b)_{\infty}$ is the [[q-Pochhammer symbol | $q$-Pochhammer symbol]]. | where $(a,b)_{\infty}$ is the [[q-Pochhammer symbol | $q$-Pochhammer symbol]]. | ||
Latest revision as of 00:56, 19 October 2014
For $0 \leq |q| < 1$, $$\theta(z;q)=\prod_{k=0}^{\infty} (1-q^kz) \left(1-\dfrac{q^{k+1}}{z} \right)=(z;q)_{\infty}\left(\frac{q}{z};q \right)_{\infty},$$ where $(a,b)_{\infty}$ is the $q$-Pochhammer symbol.
