Formula:KLS:14.08:36

<< Formula:KLS:14.08:35

formula in Al-Salam-Chihara

Formula:KLS:14.08:37 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \sum_{x=0}^\infty \frac{(1-q^{2x}a^{-2}) \qPochhammer{a^{-2},(ab)^{-1}}{q}{x}} {(1-a^{-2}) \qPochhammer{q,bqa^{-1}}{q}{x}} (ba^{-1})^xq^{x^2} \qinvAlSalamChihara{m}@{\frac12(aq^{-x}+a^{-1}q^x)}{a}{b }{q^{-1}}\qinvAlSalamChihara{n}@{\frac12(aq^{-x}+a^{-1}q^x)}{a}{b }{q^{-1}} =\frac{\qPochhammer{qa^{-2}}{q}{\infty}}{\qPochhammer{ba^{-1}q}{q}{\infty}} \qPochhammer{q,(ab)^{-1}}{q}{n} (ab)^nq^{-n^2} \Kronecker{m}{n} (ab>1,\;qb<a) }}

Proof

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Symbols List

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \Sigma}}  : sum : http://drmf.wmflabs.org/wiki/Definition:sum
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 Q_{n}}}  : Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}} -inverse Al-Salam-Chihara polynomial : http://dlmf.nist.gov/23.1
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \delta_{m,n}}}  : Kronecker delta : http://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r4

Bibliography

Equation in Section 14.8 of KLS.

URL links

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<< Formula:KLS:14.08:35

formula in Al-Salam-Chihara

Formula:KLS:14.08:37 >>