Formula:KLS:14.16:08

<< Formula:KLS:14.16:07

formula in Affine q-Krawtchouk

Formula:KLS:14.16:12 >>

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

Substitution(s)

${\displaystyle{\displaystyle{\displaystyle D(x)=-p(1-q^{x})q^{x-N}}}}$ &

${\displaystyle{\displaystyle{\displaystyle B(x)=(1-q^{x-N})(1-pq^{x+1})}}}$ &

${\displaystyle{\displaystyle{\displaystyle y(x)=K^{\mathrm{Aff}}_{n}\!\left(q^{-x};p,N;q\right)}}}$

Proof

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Symbols List

& : logical and
${\displaystyle{\displaystyle{\displaystyle K^{\mathrm{Aff}}_{n}}}}$ : affine ${\displaystyle{\displaystyle{\displaystyle q}}}$-Krawtchouk polynomial : http://drmf.wmflabs.org/wiki/Definition:AffqKrawtchouk

Bibliography

Equation in Section 14.16 of KLS.

URL links

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<< Formula:KLS:14.16:07

formula in Affine q-Krawtchouk

Formula:KLS:14.16:12 >>