Formula:KLS:09.08:69

<< Formula:KLS:09.08:68

formula in Jacobi: Special cases

Formula:KLS:09.08:70 >>

${\displaystyle{\displaystyle{\displaystyle\frac{1}{R\sqrt{\frac{1}{2}(1+R-xt)}}=\sum_{n=0}^{\infty}\frac{{\left(\frac{3}{2}\right)_{n}}}{(n+1)!}U_{n}\left(x\right)t^{n}}}}$

Substitution(s)

${\displaystyle{\displaystyle{\displaystyle R=\sqrt{1-2xt+t^{2}}}}}$

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

${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
${\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}$ : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii
${\displaystyle{\displaystyle{\displaystyle U_{n}}}}$ : 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

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

<< Formula:KLS:09.08:68

formula in Jacobi: Special cases

Formula:KLS:09.08:70 >>