Formula:KLS:14.18:16

<< Formula:KLS:14.18:15

formula in Continuous big q-Hermite

Formula:KLS:14.18:18 >>

${\displaystyle{\displaystyle{\displaystyle q^{-n}(1-q^{n})\LegendrePoly{n}@{z}=A(z)\LegendrePoly{n}@{qz}-\left[A(z)+A(z^{-1})\right]\LegendrePoly{n}@{z}{}+A(z^{-1})\LegendrePoly{n}@{q^{-1}z}}}}$

Substitution(s)

${\displaystyle{\displaystyle{\displaystyle A(z)=\frac{(1-az)}{(1-z^{2})(1-qz^{2})}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : Legendre polynomial : http://dlmf.nist.gov/18.3#T1.t1.r25

Bibliography

Equation in Section 14.18 of KLS.

URL links

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