Formula:KLS:09.08:84

<< Formula:KLS:09.08:83

formula in Jacobi: Special cases

Formula:KLS:09.08:85 >>

${\displaystyle{\displaystyle{\displaystyle W_{n}\left(x\right)=\frac{\sin\left((n+\frac{1}{2})\theta\right)}{\sin\left(\frac{1}{2}\theta\right)},x=\cos\theta}}}$

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
${\displaystyle{\displaystyle{\displaystyle\mathrm{sin}}}}$ : sine function : http://dlmf.nist.gov/4.14#E1
${\displaystyle{\displaystyle{\displaystyle\mathrm{cos}}}}$ : cosine function : http://dlmf.nist.gov/4.14#E2

Bibliography

Equation in Section 9.8 of KLS.

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<< Formula:KLS:09.08:83

formula in Jacobi: Special cases

Formula:KLS:09.08:85 >>