Formula:KLS:14.22:24

<< Formula:KLS:14.22:23

formula in q-Bessel

Formula:KLS:14.22:25 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{q\rightarrow 1}y_{n}\!\left(-\textstyle\frac{1}{2}(1-q)^{-1}x;-q^{a+1};q\right)=y_{n}\!\left(x;a\right)}}}$

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
${\displaystyle{\displaystyle{\displaystyle y_{n}}}}$ : Bessel polynomial : http://dlmf.nist.gov/18.34#E1

Bibliography

Equation in Section 14.22 of KLS.

URL links

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<< Formula:KLS:14.22:23

formula in q-Bessel

Formula:KLS:14.22:25 >>