Formula:KLS:09.08:58

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formula in Jacobi: Special cases

Formula:KLS:09.08:59 >>

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

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:09.08:57

formula in Jacobi: Special cases

Formula:KLS:09.08:59 >>