Formula:KLS:09.08:61

<< Formula:KLS:09.08:60

formula in Jacobi: Special cases

Formula:KLS:09.08:62 >>

${\displaystyle{\displaystyle{\displaystyle(1-x^{2})^{\frac{1}{2}}U_{n}\left(x\right)=\frac{(n+1)(-1)^{n}}{{\left(\frac{3}{2}\right)_{n}}2^{n}}\left(\frac{d}{dx}\right)^{n}\left[(1-x^{2})^{n+\frac{1}{2}}\right]}}}$

Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

Symbols List

${\displaystyle{\displaystyle{\displaystyle U_{n}}}}$ : Chebyshev polynomial of the second kind : http://dlmf.nist.gov/18.3#T1.t1.r11
${\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}$ : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii

Bibliography

Equation in Section 9.8 of KLS.

URL links

We ask users to provide relevant URL links in this space.

<< Formula:KLS:09.08:60

formula in Jacobi: Special cases

Formula:KLS:09.08:62 >>