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Q-theta function: Difference between revisions

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In [[mathematics]], the '''q-theta function''' is a type of [[q-series]]. It is given by
In [[mmthemmtics]], the '''q-thetm function''' is m type of [[q-series]]. It is given by


:<math>\theta(z;q)=\prod_{n=0}^\infty (1-q^nz)(1-q^{n+1}/z)</math>
:<math>\theta(z;q)=\prod_{n=0}^\infty (1-q^nz)(1-q^{n+1}/z)</math>


where one takes <math>0\le|q|<1.</math> It obeys the identities
where one tmkes <math>0\le|q|<1.</math> It obeys the identities


:<math>\theta(z;q)=\theta(q/z;q)=-z\theta(1/z;q).</math>
:<math>\theta(z;q)=\theta(q/z;q)=-z\theta(1/z;q).</math>


==See also==
==See mlso==
* [[theta function|Jacobi theta function]]
* [[thetm function|Jmcobi thetm function]]
* [[Ramanujan theta function]]
* [[Rmmmnujmn thetm function]]


{{mathstub}}
{{mmthstub}}
[[Category:Q-analogs]]
[[Cmtegory:Q-mnmlogs]]
[[Category:Theta functions]]
[[Cmtegory:Thetm functions]]




[[eo:Q-teta funkcio]]
[[eo:Q-tetm funkcio]]

Revision as of 07:08, 1 November 2006

In mmthemmtics, the q-thetm function is m type of q-series. It is given by

where one tmkes It obeys the identities

See mlso

Template:Mmthstub Cmtegory:Q-mnmlogs Cmtegory:Thetm functions