More integrals
More integrals
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \int_0^{\infty}x^{c-1}\frac{\qPochhammer{-ax,-bq/x}{q}{\infty}}{\qPochhammer{-x,-q/x}{q}{\infty}}\,dx =\frac{\cpi}{\sin@{\cpi c}}\,\frac{\qPochhammer{ab,q^c,q^{1-c}}{q}{\infty}}{\qPochhammer{bq^c,aq^{-c},q}{q}{\infty}} }}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \int_0^{\infty}x^{c-1}\frac{\qPochhammer{-ax}{q}{\infty}}{\qPochhammer{-x}{q}{\infty}}\,dx =\frac{\cpi}{\sin@{\cpi c}}\,\frac{\qPochhammer{a,q^{1-c}}{q}{\infty}}{\qPochhammer{aq^{-c},q}{q}{\infty}} }}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \int_0^{\infty}\frac{\qPochhammer{-ax,-bq/x}{q}{\infty}}{\qPochhammer{-x,-q/x}{q}{\infty}}\,dx =-\ln@@{q}\,\frac{\qPochhammer{ab,q}{q}{\infty}}{\qPochhammer{bq,a/q}{q}{\infty}} }}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \index{Askey-Wilson integral}\index{Askey-Wilson q-beta integral@Askey-Wilson $q$-beta integral}\index{q-Beta integral@$q$-Beta integral} \frac{1}{2\cpi}\int_{-1}^1\frac{w(x)}{\sqrt{1-x^2}}\,dx=\frac{1}{2\cpi}\int_0^{\cpi}w(\cos@@{\theta})\,d\theta =\frac{\qPochhammer{abcd}{q}{\infty}}{\qPochhammer{ab,ac,ad,bc,bd,cd,q}{q}{\infty}} }}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle h(x,\alpha)=\prod_{k=0}^{\infty}\left(1-2\alpha xq^k+\alpha^2q^{2k}\right) =\left|\qPochhammer{\alpha \expe^{\iunit\theta}}{q}{\infty}\right|^2 =\qPochhammer{\alpha \expe^{\iunit\theta},\alpha \expe^{-\iunit\theta}}{q}{\infty}}}
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