Formula:KLS:09.06:10

<< Formula:KLS:09.06:09

formula in Dual Hahn

Formula:KLS:09.06:14 >>

${\displaystyle{\displaystyle{\displaystyle-ny(x)=B(x)y(x+1)-\left[B(x)+D(x)\right]y(x)+D(x)y(x-1)}}}$

Substitution(s)

${\displaystyle{\displaystyle{\displaystyle D(x)=\frac{x(x+\gamma+\delta+N+1)(x+\delta)}{(2x+\gamma+\delta)(2x+\gamma+\delta+1)}}}}$ &

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

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

Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

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

We ask users to provide relevant URL links in this space.

<< Formula:KLS:09.06:09

formula in Dual Hahn

Formula:KLS:09.06:14 >>