Formula:KLS:09.01:16

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δ ⁢ W n ⁡ ( x 2 ; a , b , c , d ) δ ⁢ x 2 = - n ⁢ ( n + a + b + c + d - 1 ) ⁢ W n - 1 ⁡ ( x 2 ; a + 1 2 , b + 1 2 , c + 1 2 , d + 1 2 ) 𝛿 Wilson-polynomial-W 𝑛 superscript 𝑥 2 𝑎 𝑏 𝑐 𝑑 𝛿 superscript 𝑥 2 𝑛 𝑛 𝑎 𝑏 𝑐 𝑑 1 Wilson-polynomial-W 𝑛 1 superscript 𝑥 2 𝑎 1 2 𝑏 1 2 𝑐 1 2 𝑑 1 2 {\displaystyle{\displaystyle{\displaystyle\frac{\delta W_{n}\!\left(x^{2};a,b,% c,d\right)}{\delta x^{2}}{}=-n(n+a+b+c+d-1)W_{n-1}\!\left(x^{2};a+\textstyle% \frac{1}{2},b+\textstyle\frac{1}{2},c+\textstyle\frac{1}{2},d+\textstyle\frac{% 1}{2}\right)}}}

Proof

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Symbols List

W n subscript 𝑊 𝑛 {\displaystyle{\displaystyle{\displaystyle W_{n}}}}  : Wilson polynomial : http://dlmf.nist.gov/18.25#T1.t1.r2

Bibliography

Equation in Section 9.1 of KLS.

URL links

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