Formula:KLS:09.01:06

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W ~ n ⁡ ( x 2 ) := W ~ n ⁡ ( x 2 ; a , b , c , d ) = W n ⁡ ( x 2 ; a , b , c , d ) ( a + b ) n ⁢ ( a + c ) n ⁢ ( a + d ) n assign Wilson-polynomial-normalized-W-tilde 𝑛 superscript 𝑥 2 𝑎 𝑏 𝑐 𝑑 Wilson-polynomial-normalized-W-tilde 𝑛 superscript 𝑥 2 𝑎 𝑏 𝑐 𝑑 Wilson-polynomial-W 𝑛 superscript 𝑥 2 𝑎 𝑏 𝑐 𝑑 Pochhammer-symbol 𝑎 𝑏 𝑛 Pochhammer-symbol 𝑎 𝑐 𝑛 Pochhammer-symbol 𝑎 𝑑 𝑛 {\displaystyle{\displaystyle{\displaystyle{\tilde{W}}_{n}\!\left(x^{2}\right):% ={\tilde{W}}_{n}\!\left(x^{2};a,b,c,d\right)=\frac{W_{n}\!\left(x^{2};a,b,c,d% \right)}{{\left(a+b\right)_{n}}{\left(a+c\right)_{n}}{\left(a+d\right)_{n}}}}}}

Proof

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Symbols List

W ~ n subscript ~ 𝑊 𝑛 {\displaystyle{\displaystyle{\displaystyle{\tilde{W}}_{n}}}}  : normalized Wilson polynomial W ~ ~ 𝑊 {\displaystyle{\displaystyle{\displaystyle{\tilde{W}}}}}  : http://drmf.wmflabs.org/wiki/Definition:normWilsonWtilde
W n subscript 𝑊 𝑛 {\displaystyle{\displaystyle{\displaystyle W_{n}}}}  : Wilson polynomial : http://dlmf.nist.gov/18.25#T1.t1.r2
( a ) n subscript 𝑎 𝑛 {\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}  : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii

Bibliography

Equation in Section 9.1 of KLS.

URL links

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