Formula:KLS:09.08:83

<< Formula:KLS:09.08:82

formula in Jacobi: Special cases

Formula:KLS:09.08:84 >>

${\displaystyle{\displaystyle{\displaystyle W_{n}\left(x\right):=(2n+1)\frac{P^{(\frac{1}{2},-\frac{1}{2})}_{n}\left(x\right)}{P^{(\frac{1}{2},-\frac{1}{2})}_{n}\left(1\right)}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle W_{n}}}}$ : Chebyshev polynomial of the fourth kind : http://dlmf.nist.gov/18.3#T1.t1.r17
${\displaystyle{\displaystyle{\displaystyle P^{(\alpha,\beta)}_{n}}}}$ : Jacobi polynomial : http://dlmf.nist.gov/18.3#T1.t1.r3

Bibliography

Equation in Section 9.8 of KLS.

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<< Formula:KLS:09.08:82

formula in Jacobi: Special cases

Formula:KLS:09.08:84 >>