Formula:KLS:14.08:17

<< Formula:KLS:14.08:14

formula in Al-Salam-Chihara

Formula:KLS:14.08:18 >>

${\displaystyle{\displaystyle{\displaystyle\LegendrePoly{n}@{z}:=\frac{\left(ab;q\right)_{n}}{a^{n}}\,\qHyperrphis{3}{2}@@{q^{-n},az,az^{-1}}{ab,0}{q}{q}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : Legendre polynomial : http://dlmf.nist.gov/18.3#T1.t1.r25
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle{{}_{r}\phi_{s}}}}}$ : basic hypergeometric (or ${\displaystyle{\displaystyle{\displaystyle q}}}$-hypergeometric) function : http://dlmf.nist.gov/17.4#E1

Bibliography

Equation in Section 14.8 of KLS.

URL links

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<< Formula:KLS:14.08:14

formula in Al-Salam-Chihara

Formula:KLS:14.08:18 >>