Formula:KLS:14.13:07

<< Formula:KLS:14.13:06

formula in q-Meixner

Formula:KLS:14.13:11 >>

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

Substitution(s)

${\displaystyle{\displaystyle{\displaystyle D(x)=(1-q^{x})(1+bcq^{x})}}}$ &

${\displaystyle{\displaystyle{\displaystyle B(x)=cq^{x}(1-bq^{x+1})}}}$ &

${\displaystyle{\displaystyle{\displaystyle y(x)=M_{n}\!\left(q^{-x};b,c;q\right)}}}$

Proof

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Symbols List

& : logical and
${\displaystyle{\displaystyle{\displaystyle M_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Meixner polynomial : http://drmf.wmflabs.org/wiki/Definition:qMeixner

Bibliography

Equation in Section 14.13 of KLS.

URL links

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formula in q-Meixner

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