Formula:KLS:14.18:15

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formula in Continuous big q-Hermite

Formula:KLS:14.18:16 >>

${\displaystyle{\displaystyle{\displaystyle\LegendrePoly{n}@{z}:=a^{-n}\,\qHyperrphis{3}{2}@@{q^{-n},az,az^{-1}}{0,0}{q}{q}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : Legendre polynomial : http://dlmf.nist.gov/18.3#T1.t1.r25
${\displaystyle{\displaystyle{\displaystyle{{}_{r}\phi_{s}}}}}$ : basic hypergeometric (or ${\displaystyle{\displaystyle{\displaystyle q}}}$-hypergeometric) function : http://dlmf.nist.gov/17.4#E1

Bibliography

Equation in Section 14.18 of KLS.

URL links

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