Formula:KLS:14.14:07

<< Formula:KLS:14.14:06

formula in Quantum q-Krawtchouk

Formula:KLS:14.14:11 >>

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

Substitution(s)

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

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

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

Proof

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Symbols List

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

Bibliography

Equation in Section 14.14 of KLS.

URL links

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formula in Quantum q-Krawtchouk

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