Formula:KLS:09.08:23

<< Formula:KLS:09.08:22

formula in Jacobi

Formula:KLS:09.08:24 >>

${\displaystyle{\displaystyle{\displaystyle P^{(\alpha,\beta)}_{n}\left(x\right)=\frac{1}{n!}\sum_{k=0}^{n}\frac{{\left(-n\right)_{k}}}{k!}{\left(n+\alpha+\beta+1\right)_{k}}{\left(\alpha+k+1\right)_{n-k}}\left(\frac{1-x}{2}\right)^{k}}}}$

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

${\displaystyle{\displaystyle{\displaystyle P^{(\alpha,\beta)}_{n}}}}$ : Jacobi polynomial : http://dlmf.nist.gov/18.3#T1.t1.r3
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
${\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}$ : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii

Bibliography

Equation in Section 9.8 of KLS.

URL links

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

<< Formula:KLS:09.08:22

formula in Jacobi

Formula:KLS:09.08:24 >>