Gold 10

Legendre polynomials

Gold ID: 10
Link: https://sigir21.wmflabs.org/wiki/Legendre_polynomials#math.60.57
Formula: ${\frac {1}{\left|\mathbf {x} -\mathbf {x} '\right|}}={\frac {1}{\sqrt {r^{2}+{r'}^{2}-2r{r'}\cos \gamma }}}=\sum _{\ell =0}^{\infty }{\frac {{r'}^{\ell }}{r^{\ell +1}}}P_{\ell }(\cos \gamma )$
TeX Source: \frac{1}{\left| \mathbf{x}-\mathbf{x}' \right|} = \frac{1}{\sqrt{r^2+{r'}^2-2r{r'}\cos\gamma}} = \sum_{\ell=0}^\infty \frac{{r'}^\ell}{r^{\ell+1}} P_\ell(\cos \gamma)

Translation Results
Semantic LaTeX	Mathematica Translation	Maple Translations
		-

Translation: \frac{1}{|\mathbf{x} - \mathbf{x} '|} = \frac{1}{\sqrt{r^2+{r'}^2-2r{r'}\cos\gamma}} = \sum_{\ell=0}^\infty \frac{{r'}^\ell}{r^{\ell+1}} \LegendrepolyP{\ell}@{\cos \gamma}
Expected (Gold Entry): \frac{1}{|\mathbf{x} - \mathbf{x} '|} = \frac{1}{\sqrt{r^2+{r'}^2-2r{r'}\cos\gamma}} = \sum_{\ell=0}^\infty \frac{{r'}^\ell}{r^{\ell+1}} \LegendrepolyP{\ell}@{\cos \gamma}

Translation
Expected (Gold Entry): Divide[1, Abs[x - x\[Prime]]] == Divide[1, Sqrt[r^2+(r\[Prime])^(2)-2*r*r\[Prime] Cos[\[Gamma]]]] == Sum[Divide[(r\[Prime])^(\[ScriptL]), r^(\[ScriptL]+1)]*LegendreP[\[ScriptL], Cos[\[Gamma]]], {\[ScriptL], 0, Infinity}]