Formula:KLS:09.06:16

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formula in Dual Hahn

Formula:KLS:09.06:17 >>

${\displaystyle{\displaystyle{\displaystyle(x+\gamma)(x+\gamma+\delta)(N+1-x)R_{n}\!\left(\lambda(x);\gamma,\delta,N\right){}-x(x+\gamma+\delta+N+1)(x+\delta)R_{n}\!\left(\lambda(x-1);\gamma,\delta,N\right){}=\gamma(N+1)(2x+\gamma+\delta)R_{n+1}\!\left(\lambda(x);\gamma-1,\delta,N+1\right)}}}$

Substitution(s)

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

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle R_{n}}}}$ : 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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formula in Dual Hahn

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