Formula:KLS:09.07:12

<< Formula:KLS:09.07:10

formula in Meixner-Pollaczek

Formula:KLS:09.07:13 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \omega(x;\lambda,\phi)\MeixnerPollaczek{\lambda}{n}@{x}{\phi}=\frac{(-1)^n}{n!} \left(\frac{\delta}{\delta x}\right)^n\left[\omega(x;\lambda+\textstyle\frac{1}{2}n,\phi)\right] }}

Substitution(s)

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \omega(x;\lambda,\phi)=\EulerGamma@{\lambda+\iunit x}\EulerGamma@{\lambda-\iunit x}\expe^{(2\phi-\cpi)x}}}

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^{(\alpha)}_{n}}}  : Meixner-Pollaczek polynomial : http://dlmf.nist.gov/18.19#P3.p1
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \Gamma}}  : Euler's gamma function : http://dlmf.nist.gov/5.2#E1
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 \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 \pi}}  : ratio of a circle's circumference to its diameter : http://dlmf.nist.gov/5.19.E4

Bibliography

Equation in Section 9.7 of KLS.

URL links

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<< Formula:KLS:09.07:10

formula in Meixner-Pollaczek

Formula:KLS:09.07:13 >>