Formula:KLS:14.04:11

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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle x\monicctsqHahn{n}@@{x}{a}{b}{c}{d}{q}=\monicctsqHahn{n+1}@@{x}{a}{b}{c}{d}{q}+\frac{1}{2}\left[a\expe^{\iunit\phi}+a^{-1}\expe^{-\iunit\phi}-(A_n+C_n)\right]\monicctsqHahn{n}@@{x}{a}{b}{c}{d}{q} {}+\frac{1}{4}A_{n-1}C_n\monicctsqHahn{n-1}@@{x}{a}{b}{c}{d}{q} }}

Substitution(s)

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle C_n=\frac{a\expe^{\iunit\phi}(1-q^n)(1-bcq^{n-1})(1-bdq^{n-1})(1-cd\expe^{-2\iunit\phi}q^{n-1})}{(1-abcdq^{2n-2})(1-abcdq^{2n-1})}}} &
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle A_n=\frac{(1-ab\expe^{2\iunit\phi}q^n)(1-acq^n)(1-adq^n)(1-abcdq^{n-1})}{a\expe^{\iunit\phi}(1-abcdq^{2n-1})(1-abcdq^{2n})}}}


Proof

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Symbols List

& : logical and
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle {\widehat p}_{n}}}  : monic continuous Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}} -Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:monicctsqHahn
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

Bibliography

Equation in Section 14.4 of KLS.

URL links

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