Formula:KLS:14.22:10

<< Formula:KLS:14.22:09

formula in q-Bessel

Formula:KLS:14.22:12 >>

${\displaystyle{\displaystyle{\displaystyle-q^{-n}(1-q^{n})(1+aq^{n})xy(x){}=axy(qx)-(ax+1-x)y(x)+(1-x)y(q^{-1}x)}}}$

Substitution(s)

${\displaystyle{\displaystyle{\displaystyle y(x)=y_{n}\!\left(x;a;q\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle y_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Bessel polynomial : http://drmf.wmflabs.org/wiki/Definition:qBessel

Bibliography

Equation in Section 14.22 of KLS.

URL links

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<< Formula:KLS:14.22:09

formula in q-Bessel

Formula:KLS:14.22:12 >>