Formula:KLS:14.10:95

<< Formula:KLS:14.10:89

formula in Continuous q-Jacobi: Special cases

Formula:KLS:14.10:96 >>

${\displaystyle{\displaystyle{\displaystyle 2(1-q^{n+\frac{1}{2}})xP_{n}\!\left(x|q\right)=q^{-\frac{1}{4}}(1-q^{n+1})P_{n+1}\!\left(x|q\right)+q^{\frac{1}{4}}(1-q^{n})P_{n-1}\!\left(x|q\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : continuous ${\displaystyle{\displaystyle{\displaystyle q}}}$-Legendre polynomial : http://drmf.wmflabs.org/wiki/Definition:ctsqLegendre

Bibliography

Equation in Section 14.10 of KLS.

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<< Formula:KLS:14.10:89

formula in Continuous q-Jacobi: Special cases

Formula:KLS:14.10:96 >>