Formula:KLS:09.08:59

<< Formula:KLS:09.08:58

formula in Jacobi: Special cases

Formula:KLS:09.08:60 >>

${\displaystyle{\displaystyle{\displaystyle\frac{d}{dx}\left[\left(1-x^{2}\right)^{\frac{1}{2}}U_{n}\left(x\right)\right]=-(n+1)\left(1-x^{2}\right)^{-\frac{1}{2}}T_{n+1}\left(x\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle U_{n}}}}$ : Chebyshev polynomial of the second kind : http://dlmf.nist.gov/18.3#T1.t1.r11
${\displaystyle{\displaystyle{\displaystyle T_{n}}}}$ : Chebyshev polynomial of the first kind : http://dlmf.nist.gov/18.3#T1.t1.r8

Bibliography

Equation in Section 9.8 of KLS.

URL links

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<< Formula:KLS:09.08:58

formula in Jacobi: Special cases

Formula:KLS:09.08:60 >>