Formula:KLS:09.11:11

<< Formula:KLS:09.11:10

formula in Krawtchouk

Formula:KLS:09.11:12 >>

${\displaystyle{\displaystyle{\displaystyle\nabla\left[\binomial{N}{x}\left(\frac{p}{1-p}\right)^{x}K_{n}\!\left(x;p,N\right)\right]=\binomial{N+1}{x}\left(\frac{p}{1-p}\right)^{x}K_{n+1}\!\left(x;p,N+1\right)}}}$

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

${\displaystyle{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{n}{k}}}}$ : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1
${\displaystyle{\displaystyle{\displaystyle K_{n}}}}$ : Krawtchouk polynomial : http://dlmf.nist.gov/18.19#T1.t1.r6

Bibliography

Equation in Section 9.11 of KLS.

URL links

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

<< Formula:KLS:09.11:10

formula in Krawtchouk

Formula:KLS:09.11:12 >>