Formula:KLS:09.08:56

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formula in Jacobi: Special cases

Formula:KLS:09.08:57 >>

${\displaystyle{\displaystyle{\displaystyle(1-x^{2})y^{\prime\prime}(x)-3xy^{\prime}(x)+n(n+2)y(x)=0}}}$

Substitution(s)

${\displaystyle{\displaystyle{\displaystyle y(x)=U_{n}\left(x\right)}}}$

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

Bibliography

Equation in Section 9.8 of KLS.

URL links

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<< Formula:KLS:09.08:55

formula in Jacobi: Special cases

Formula:KLS:09.08:57 >>