Coulomb Functions - 33.9 Expansions in Series of Bessel Functions

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
33.9.E2	${\displaystyle{\displaystyle\frac{k(k+2\ell+1)}{2k+2\ell+1}a_{k}-2\eta a_{k-1}+\frac{(k-2)(k+2\ell-1)}{2k+2\ell-3}a_{k-2}=0}}$ \frac{k(k+2\ell+1)}{2k+2\ell+1}a_{k}-2\eta a_{k-1}+\frac{(k-2)(k+2\ell-1)}{2k+2\ell-3}a_{k-2} = 0		(k*(k + 2*ell + 1))/(2*k + 2*ell + 1)*a[k]- 2*eta*a[k - 1]+((k - 2)*(k + 2*ell - 1))/(2*k + 2*ell - 3)*a[k - 2] = 0	Divide[k*(k + 2*\[ScriptL]+ 1),2*k + 2*\[ScriptL]+ 1]*Subscript[a, k]- 2*\[Eta]*Subscript[a, k - 1]+Divide[(k - 2)*(k + 2*\[ScriptL]- 1),2*k + 2*\[ScriptL]- 3]*Subscript[a, k - 2] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
33.9.E5	${\displaystyle{\displaystyle 4\eta^{2}(k-2\ell)b_{k+1}+kb_{k-1}+b_{k-2}=0}}$ 4\eta^{2}(k-2\ell)b_{k+1}+kb_{k-1}+b_{k-2} = 0	${\displaystyle{\displaystyle k=2\ell+2}}$	4*(eta)^(2)*(k - 2*ell)*b[k + 1]+ k*b[k - 1]+ b[k - 2] = 0	4*\[Eta]^(2)*(k - 2*\[ScriptL])*Subscript[b, k + 1]+ k*Subscript[b, k - 1]+ Subscript[b, k - 2] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-