Formula:KLS:09.08:75

<< Formula:KLS:09.08:74

formula in Jacobi: Special cases

Formula:KLS:09.08:76 >>

${\displaystyle{\displaystyle{\displaystyle U_{n}\left(x\right)=\frac{\sin\left(n+1\right)\theta}{\sin\theta}}}}$

Substitution(s)

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

Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

Symbols List

${\displaystyle{\displaystyle{\displaystyle U_{n}}}}$ : Chebyshev polynomial of the second kind : http://dlmf.nist.gov/18.3#T1.t1.r11
${\displaystyle{\displaystyle{\displaystyle\mathrm{sin}}}}$ : 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.

URL links

We ask users to provide relevant URL links in this space.

<< Formula:KLS:09.08:74

formula in Jacobi: Special cases

Formula:KLS:09.08:76 >>