Formula:KLS:14.29:25

<< Formula:KLS:14.29:24

formula in Discrete q-Hermite II

Orthogonal Polynomials

${\displaystyle{\displaystyle{\displaystyle P^{(\alpha,\beta)}_{n}\!\left(-x|q\right)=(-1)^{n}q^{\frac{1}{2}(\alpha-\beta)n}P^{(\beta,\alpha)}_{n}\!\left(x|q\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle P^{(\alpha,\beta)}_{n}}}}$ : continuous ${\displaystyle{\displaystyle{\displaystyle q}}}$-Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:ctsqJacobi

Bibliography

Equation in Section 14.29 of KLS.

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<< Formula:KLS:14.29:24

formula in Orthogonal Polynomials

Orthogonal Polynomials