Formula:KLS:09.05:07

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formula in Hahn

Formula:KLS:09.05:08 >>

${\displaystyle{\displaystyle{\displaystyle x{\widehat{Q}}_{n}\!\left(x\right)={\widehat{Q}}_{n+1}\!\left(x\right)+\left(A_{n}+C_{n}\right){\widehat{Q}}_{n}\!\left(x\right)+A_{n-1}C_{n}{\widehat{Q}}_{n-1}\!\left(x\right)}}}$

Substitution(s)

${\displaystyle{\displaystyle{\displaystyle C_{n}=\frac{n(n+\alpha+\beta+N+1)(n+\beta)}{(2n+\alpha+\beta)(2n+\alpha+\beta+1)}}}}$ &
${\displaystyle{\displaystyle{\displaystyle A_{n}=\frac{(n+\alpha+\beta+1)(n+\alpha+1)(N-n)}{(2n+\alpha+\beta+1)(2n+\alpha+\beta+2)}}}}$

Proof

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Symbols List

& : logical and
${\displaystyle{\displaystyle{\displaystyle{\widehat{Q}}_{n}}}}$ : monic Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:monicHahn

Bibliography

Equation in Section 9.5 of KLS.

URL links

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<< Formula:KLS:09.05:04

formula in Hahn

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