Formula:KLS:14.03:32

<< Formula:KLS:14.03:31

formula in Continuous dual q-Hahn

Formula:KLS:14.03:33 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{q\rightarrow 1}\frac{p_{n}\!\left(\frac{1}{2}\left(q^{\mathrm{i}x}+q^{-\mathrm{i}x}\right);q^{a},q^{b},q^{c}|q\right)}{(1-q)^{2n}}=S_{n}\!\left(x^{2};a,b,c\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : continuous dual ${\displaystyle{\displaystyle{\displaystyle q}}}$-Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:ctsdualqHahn
${\displaystyle{\displaystyle{\displaystyle\mathrm{i}}}}$ : imaginary unit : http://dlmf.nist.gov/1.9.i
${\displaystyle{\displaystyle{\displaystyle S_{n}}}}$ : continuous dual Hahn polynomial : http://dlmf.nist.gov/18.25#T1.t1.r3

Bibliography

Equation in Section 14.3 of KLS.

URL links

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<< Formula:KLS:14.03:31

formula in Continuous dual q-Hahn

Formula:KLS:14.03:33 >>