Formula:KLS:09.11:36

<< Formula:KLS:09.11:35

formula in Krawtchouk

Formula:KLS:09.11:37 >>

${\displaystyle{\displaystyle{\displaystyle K_{2m+1}\!\left(x+N+1;\frac{1}{2},2N+1\right)=\frac{{\left(\tfrac{3}{2}\right)_{m}}}{{\left(-N-\frac{1}{2}\right)_{m+1}}}(x+\frac{1}{2})R_{m}\!\left(x(x+1);\frac{1}{2},-\frac{1}{2},N\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle K_{n}}}}$ : Krawtchouk polynomial : http://dlmf.nist.gov/18.19#T1.t1.r6
${\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}$ : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii
${\displaystyle{\displaystyle{\displaystyle R_{n}}}}$ : dual Hahn polynomial : http://dlmf.nist.gov/18.25#T1.t1.r5

Bibliography

Equation in Section 9.11 of KLS.

URL links

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<< Formula:KLS:09.11:35

formula in Krawtchouk

Formula:KLS:09.11:37 >>