Formula:KLS:14.22:23

<< Formula:KLS:14.22:22

formula in q-Bessel

Formula:KLS:14.22:24 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{a\rightarrow\infty}y_{n}\!\left(a^{-1}x;a;q\right)=\left(q;q\right)_{n}S_{n}\!\left(x;q\right)}}}$

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
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle S_{n}}}}$ : Stieltjes-Wigert polynomial : http://drmf.wmflabs.org/wiki/Definition:StieltjesWigert

Bibliography

Equation in Section 14.22 of KLS.

URL links

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<< Formula:KLS:14.22:22

formula in q-Bessel

Formula:KLS:14.22:24 >>