Coulomb Functions - 33.12 Asymptotic Expansions for Large

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
33.12#Ex6	${\displaystyle{\displaystyle B_{1}=-\tfrac{1}{5}x}}$ B_{1} = -\tfrac{1}{5}x		B[1] = -(1)/(5)*x	Subscript[B, 1] == -Divide[1,5]*x	Skipped - no semantic math	Skipped - no semantic math	-	-
33.12#Ex7	${\displaystyle{\displaystyle B_{2}=\tfrac{1}{350}(7x^{5}-30x^{2})}}$ B_{2} = \tfrac{1}{350}(7x^{5}-30x^{2})		B[2] = (1)/(350)*(7*(x)^(5)- 30*(x)^(2))	Subscript[B, 2] == Divide[1,350]*(7*(x)^(5)- 30*(x)^(2))	Skipped - no semantic math	Skipped - no semantic math	-	-
33.12#Ex8	${\displaystyle{\displaystyle B_{3}=\tfrac{1}{15750}(264x^{6}-290x^{3}-560)}}$ B_{3} = \tfrac{1}{15750}(264x^{6}-290x^{3}-560)		B[3] = (1)/(15750)*(264*(x)^(6)- 290*(x)^(3)- 560)	Subscript[B, 3] == Divide[1,15750]*(264*(x)^(6)- 290*(x)^(3)- 560)	Skipped - no semantic math	Skipped - no semantic math	-	-
33.12.E8	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}=\left(4\eta^{2}\left(\frac{1-z}{z}\right)+\frac{\ell(\ell+1)}{z^{2}}\right)w}}$ \deriv[2]{w}{z} = \left(4\eta^{2}\left(\frac{1-z}{z}\right)+\frac{\ell(\ell+1)}{z^{2}}\right)w		diff(w, [z$(2)]) = (4*(eta((1 - z)/(z)))^(2)+(ell*(ell + 1))/((z)^(2)))*w	D[w, {z, 2}] == (4*(\[Eta][Divide[1 - z,z]])^(2)+Divide[\[ScriptL]*(\[ScriptL]+ 1),(z)^(2)])*w	Failure	Failure	Error	Failed [296 / 300] Result: Complex[-3.7320508075688767, 1.5358983848622458] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ℓ, 1], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-7.196152422706632, 3.535898384862246] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ℓ, 2], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data