Formula:KLS:14.10:63: Difference between revisions

From DRMF
Jump to navigation Jump to search
imported>SeedBot
DRMF
 
m Move page script moved page Formula:KLS:14.10:63 to F:KLS:14.10:63
 
(No difference)

Latest revision as of 08:37, 22 December 2019


( β 2 ; q ) n ⁢ p n ⁡ ( x ; β 1 2 , β 1 2 ⁢ q 1 2 , - β 1 2 , - β 1 2 ⁢ q 1 2 | q ) ( β ⁢ q 1 2 , - β , - β ⁢ q 1 2 , q ; q ) n = C n ⁡ ( x ; β | q ) q-Pochhammer-symbol superscript 𝛽 2 𝑞 𝑛 Askey-Wilson-polynomial-p 𝑛 𝑥 superscript 𝛽 1 2 superscript 𝛽 1 2 superscript 𝑞 1 2 superscript 𝛽 1 2 superscript 𝛽 1 2 superscript 𝑞 1 2 𝑞 q-Pochhammer-symbol 𝛽 superscript 𝑞 1 2 𝛽 𝛽 superscript 𝑞 1 2 𝑞 𝑞 𝑛 continuous-q-ultraspherical-Rogers-polynomial 𝑛 𝑥 𝛽 𝑞 {\displaystyle{\displaystyle{\displaystyle\frac{\left(\beta^{2};q\right)_{n}p_% {n}\!\left(x;\beta^{\frac{1}{2}},\beta^{\frac{1}{2}}q^{\frac{1}{2}},-\beta^{% \frac{1}{2}},-\beta^{\frac{1}{2}}q^{\frac{1}{2}}\,|\,q\right)}{\left(\beta q^{% \frac{1}{2}},-\beta,-\beta q^{\frac{1}{2}},q;q\right)_{n}}=C_{n}\!\left(x;% \beta\,|\,q\right)}}}

Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

Symbols List

( 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
p n subscript 𝑝 𝑛 {\displaystyle{\displaystyle{\displaystyle p_{n}}}}  : Askey-Wilson polynomial : http://dlmf.nist.gov/18.28#E1
C n subscript 𝐶 𝑛 {\displaystyle{\displaystyle{\displaystyle C_{n}}}}  : continuous q 𝑞 {\displaystyle{\displaystyle{\displaystyle q}}} -ultraspherical/Rogers polynomial : http://dlmf.nist.gov/18.28#E13

Bibliography

Equation in Section 14.10 of KLS.

URL links

We ask users to provide relevant URL links in this space.


Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Formula:KLS:14.10:63&oldid=4837"