Formula:KLS:09.08:60

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formula in Jacobi: Special cases

Formula:KLS:09.08:61 >>

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

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle T_{n}}}}$ : Chebyshev polynomial of the first kind : http://dlmf.nist.gov/18.3#T1.t1.r8
${\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}$ : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii

Bibliography

Equation in Section 9.8 of KLS.

URL links

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formula in Jacobi: Special cases

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