Formula:KLS:09.08:74

<< Formula:KLS:09.08:73

formula in Jacobi: Special cases

Formula:KLS:09.08:75 >>

${\displaystyle{\displaystyle{\displaystyle T_{n}\left(x\right)=\cos\left(n\theta\right)}}}$

Substitution(s)

${\displaystyle{\displaystyle{\displaystyle x=\cos\theta}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle T_{n}}}}$ : Chebyshev polynomial of the first kind : http://dlmf.nist.gov/18.3#T1.t1.r8
${\displaystyle{\displaystyle{\displaystyle\mathrm{cos}}}}$ : cosine function : http://dlmf.nist.gov/4.14#E2

Bibliography

Equation in Section 9.8 of KLS.

URL links

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<< Formula:KLS:09.08:73

formula in Jacobi: Special cases

Formula:KLS:09.08:75 >>