Formula:KLS:09.08:50

<< Formula:KLS:09.08:49

formula in Jacobi: Special cases

Formula:KLS:09.08:51 >>

${\displaystyle{\displaystyle{\displaystyle 2xU_{n}\left(x\right)=U_{n+1}\left(x\right)+U_{n-1}\left(x\right),\quad U_{0}\left(x\right)=1\quad\textrm{and}\quad U_{1}\left(x\right)=2x}}}$

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

Bibliography

Equation in Section 9.8 of KLS.

URL links

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<< Formula:KLS:09.08:49

formula in Jacobi: Special cases

Formula:KLS:09.08:51 >>