Formula:KLS:14.19:02

<< Formula:KLS:14.19:01

formula in Continuous q-Laguerre

Formula:KLS:14.19:03 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \ctsqLaguerre{\alpha}{n}@{x}{q}=\frac{\qPochhammer{q^{\frac{1}{2}\alpha+\frac{3}{4}}\expe^{-\iunit\theta}}{q}{n}}{\qPochhammer{q}{q}{n}} q^{(\frac{1}{2}\alpha+\frac{1}{4})n}\expe^{\iunit n\theta} {}\qHyperrphis{2}{1}@@{q^{-n},q^{\frac{1}{2}\alpha+\frac{1}{4}}\expe^{\iunit\theta}} {q^{-\frac{1}{2}\alpha+\frac{1}{4}-n}\expe^{\iunit\theta}} {q}{q^{-\frac{1}{2}\alpha+\frac{1}{4}}\expe^{-\iunit\theta}} }}

Proof

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Symbols List

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle P^{(n)}_{\alpha}}}  : continuous Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}} -Laguerre polynomial : http://drmf.wmflabs.org/wiki/Definition:ctsqLaguerre
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle (a;q)_n}}  : Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}} -Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mathrm{e}}}  : the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mathrm{i}}}  : imaginary unit : http://dlmf.nist.gov/1.9.i
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle {{}_{r}\phi_{s}}}}  : basic hypergeometric (or Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}} -hypergeometric) function : http://dlmf.nist.gov/17.4#E1

Bibliography

Equation in Section 14.19 of KLS.

URL links

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<< Formula:KLS:14.19:01

formula in Continuous q-Laguerre

Formula:KLS:14.19:03 >>