Formula:KLS:14.01:12: Difference between revisions

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Latest revision as of 08:36, 22 December 2019


p ~ n ⁡ ( x ) := p ~ n ⁡ ( x ; a , b , c , d | q ) = a n ⁢ p n ⁡ ( x ; a , b , c , d | q ) ( a ⁢ b , a ⁢ c , a ⁢ d ; q ) n assign Askey-Wilson-polynomial-normalized-p-tilde 𝑛 𝑥 𝑎 𝑏 𝑐 𝑑 𝑞 Askey-Wilson-polynomial-normalized-p-tilde 𝑛 𝑥 𝑎 𝑏 𝑐 𝑑 𝑞 superscript 𝑎 𝑛 Askey-Wilson-polynomial-p 𝑛 𝑥 𝑎 𝑏 𝑐 𝑑 𝑞 q-Pochhammer-symbol 𝑎 𝑏 𝑎 𝑐 𝑎 𝑑 𝑞 𝑛 {\displaystyle{\displaystyle{\displaystyle{\tilde{p}}_{n}\!\left(x\right):={% \tilde{p}}_{n}\!\left(x;a,b,c,d\,|\,q\right)=\frac{a^{n}p_{n}\!\left(x;a,b,c,d% \,|\,q\right)}{\left(ab,ac,ad;q\right)_{n}}}}}

Proof

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Symbols List

p ~ n subscript ~ 𝑝 𝑛 {\displaystyle{\displaystyle{\displaystyle{\tilde{p}}_{n}}}}  : normalized Askey-Wilson polynomial p ~ ~ 𝑝 {\displaystyle{\displaystyle{\displaystyle{\tilde{p}}}}}  : http://drmf.wmflabs.org/wiki/Definition:normAskeyWilsonptilde
p n subscript 𝑝 𝑛 {\displaystyle{\displaystyle{\displaystyle p_{n}}}}  : Askey-Wilson polynomial : http://dlmf.nist.gov/18.28#E1
( a ; q ) n subscript 𝑎 𝑞 𝑛 {\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}  : q 𝑞 {\displaystyle{\displaystyle{\displaystyle q}}} -Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1

Bibliography

Equation in Section 14.1 of KLS.

URL links

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