Coulomb Functions - 33.19 Power-Series Expansions in

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
33.19.E4	${\displaystyle{\displaystyle\gamma_{k}-\gamma_{k-1}+\tfrac{1}{4}(k-1)(k-2\ell-2)\epsilon\gamma_{k-2}=0}}$ \gamma_{k}-\gamma_{k-1}+\tfrac{1}{4}(k-1)(k-2\ell-2)\epsilon\gamma_{k-2} = 0		gamma[k]- gamma[k - 1]+(1)/(4)*(k - 1)*(k - 2*ell - 2)*epsilon*gamma[k - 2] = 0	Subscript[\[Gamma], k]- Subscript[\[Gamma], k - 1]+Divide[1,4]*(k - 1)*(k - 2*\[ScriptL]- 2)*\[Epsilon]*Subscript[\[Gamma], k - 2] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
33.19.E6	${\displaystyle{\displaystyle k(k+2\ell+1)\delta_{k}+2\delta_{k-1}+\epsilon\delta_{k-2}+2(2k+2\ell+1)A(\epsilon,\ell)\alpha_{k}=0}}$ k(k+2\ell+1)\delta_{k}+2\delta_{k-1}+\epsilon\delta_{k-2}+2(2k+2\ell+1)A(\epsilon,\ell)\alpha_{k} = 0		k*(k + 2*ell + 1)*delta[k]+ 2*delta[k - 1]+ epsilon*delta[k - 2]+ 2*(2*k + 2*ell + 1)*(product(1 + epsilon*(k)^(2), k = 0..ell))*alpha[k] = 0	k*(k + 2*\[ScriptL]+ 1)*Subscript[\[Delta], k]+ 2*Subscript[\[Delta], k - 1]+ \[Epsilon]*Subscript[\[Delta], k - 2]+ 2*(2*k + 2*\[ScriptL]+ 1)*(Product[1 + \[Epsilon]*(k)^(2), {k, 0, \[ScriptL]}, GenerateConditions->None])*Subscript[\[Alpha], k] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
33.19.E7	${\displaystyle{\displaystyle\beta_{k}-\beta_{k-1}+\tfrac{1}{4}(k-1)(k-2\ell-2)\epsilon\beta_{k-2}+\tfrac{1}{2}(k-1)\epsilon\gamma_{k-2}=0}}$ \beta_{k}-\beta_{k-1}+\tfrac{1}{4}(k-1)(k-2\ell-2)\epsilon\beta_{k-2}+\tfrac{1}{2}(k-1)\epsilon\gamma_{k-2} = 0		beta[k]- beta[k - 1]+(1)/(4)*(k - 1)*(k - 2*ell - 2)*epsilon*beta[k - 2]+(1)/(2)*(k - 1)*epsilon*gamma[k - 2] = 0	Subscript[\[Beta], k]- Subscript[\[Beta], k - 1]+Divide[1,4]*(k - 1)*(k - 2*\[ScriptL]- 2)*\[Epsilon]*Subscript[\[Beta], k - 2]+Divide[1,2]*(k - 1)*\[Epsilon]*Subscript[\[Gamma], k - 2] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-