Formula:KLS:09.06:04

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formula in Dual Hahn

Formula:KLS:09.06:05 >>

${\displaystyle{\displaystyle{\displaystyle\lambda(x)R_{n}\!\left(\lambda(x)\right)=A_{n}R_{n+1}\!\left(\lambda(x)\right)-\left(A_{n}+C_{n}\right)R_{n}\!\left(\lambda(x)\right)+C_{n}R_{n-1}\!\left(\lambda(x)\right)}}}$

Substitution(s)

${\displaystyle{\displaystyle{\displaystyle C_{n}=n(n-\delta-N-1)}}}$ &

${\displaystyle{\displaystyle{\displaystyle A_{n}=(n+\gamma+1)(n-N)}}}$ &

${\displaystyle{\displaystyle{\displaystyle\lambda(x)=x(x+\gamma+\delta+1)}}}$

Proof

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Symbols List

& : logical and
${\displaystyle{\displaystyle{\displaystyle R_{n}}}}$ : dual Hahn polynomial : http://dlmf.nist.gov/18.25#T1.t1.r5

Bibliography

Equation in Section 9.6 of KLS.

URL links

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