2.7

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
2.7.E3	${\displaystyle{\displaystyle Q(\alpha)\equiv\alpha(\alpha-1)+f_{0}\alpha+g_{0}=0}}$ Q(\alpha)\defeq\alpha(\alpha-1)+f_{0}\alpha+g_{0} = 0		Q(alpha) = alpha*(alpha - 1)+ f[0]*alpha + g[0] = 0	Q[\[Alpha]] == \[Alpha]*(\[Alpha]- 1)+ Subscript[f, 0]*\[Alpha]+ Subscript[g, 0] == 0	Failure	Failure	Error	Failed [299 / 300] Result: False Test Values: {Rule[Q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[Subscript[f, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: False Test Values: {Rule[Q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[Subscript[f, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, 0], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
2.7.E4	${\displaystyle{\displaystyle w_{j}(z)=(z-z_{0})^{\alpha_{j}}\sum_{s=0}^{\infty}a_{s,j}(z-z_{0})^{s}}}$ w_{j}(z) = (z-z_{0})^{\alpha_{j}}\sum_{s=0}^{\infty}a_{s,j}(z-z_{0})^{s}		w[j](z) = (z - z[0])^(alpha[j])* sum(a[s , j]*(z - z[0])^(s), s = 0..infinity)	Subscript[w, j][z] == (z - Subscript[z, 0])^(Subscript[\[Alpha], j])* Sum[Subscript[a, s , j]*(z - Subscript[z, 0])^(s), {s, 0, Infinity}, GenerateConditions->None]	Skipped - no semantic math	Skipped - no semantic math	-	-
2.7.E5	${\displaystyle{\displaystyle Q(\alpha_{j}+s)a_{s,j}=-\sum_{r=0}^{s-1}\left((\alpha_{j}+r)f_{s-r}+g_{s-r}\right)a_{r,j}}}$ Q(\alpha_{j}+s)a_{s,j} = -\sum_{r=0}^{s-1}\left((\alpha_{j}+r)f_{s-r}+g_{s-r}\right)a_{r,j}		Q*(alpha[j]+ s)*a[s , j] = - sum(((alpha[j]+ r)*f[s - r]+ g[s - r])*a[r , j], r = 0..s - 1)	Q*(Subscript[\[Alpha], j]+ s)*Subscript[a, s , j] == - Sum[((Subscript[\[Alpha], j]+ r)*Subscript[f, s - r]+ Subscript[g, s - r])*Subscript[a, r , j], {r, 0, s - 1}, GenerateConditions->None]	Skipped - no semantic math	Skipped - no semantic math	-	-
2.7.E9	${\displaystyle{\displaystyle\lambda^{2}+f_{0}\lambda+g_{0}=0}}$ \lambda^{2}+f_{0}\lambda+g_{0} = 0		(lambda)^(2)+ f[0]*lambda + g[0] = 0	\[Lambda]^(2)+ Subscript[f, 0]*\[Lambda]+ Subscript[g, 0] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
2.7.E10	${\displaystyle{\displaystyle\mu_{j}=-(f_{1}\lambda_{j}+g_{1})/(f_{0}+2\lambda_{j})}}$ \mu_{j} = -(f_{1}\lambda_{j}+g_{1})/(f_{0}+2\lambda_{j})		mu[j] = -(f[1]*lambda[j]+ g[1])/(f[0]+ 2*lambda[j])	Subscript[\[Mu], j] == -(Subscript[f, 1]*Subscript[\[Lambda], j]+ Subscript[g, 1])/(Subscript[f, 0]+ 2*Subscript[\[Lambda], j])	Skipped - no semantic math	Skipped - no semantic math	-	-
2.7.E11	${\displaystyle{\displaystyle(f_{0}+2\lambda_{j})sa_{s,j}=(s-\mu_{j})(s-1-\mu_{j})a_{s-1,j}+\sum_{r=1}^{s}\left(\lambda_{j}f_{r+1}+g_{r+1}-(s-r-\mu_{j})f_{r}\right)a_{s-r,j}}}$ (f_{0}+2\lambda_{j})sa_{s,j} = (s-\mu_{j})(s-1-\mu_{j})a_{s-1,j}+\sum_{r=1}^{s}\left(\lambda_{j}f_{r+1}+g_{r+1}-(s-r-\mu_{j})f_{r}\right)a_{s-r,j}		(f[0]+ 2*lambda[j])*s*a[s , j] = (s - mu[j])*(s - 1 - mu[j])*a[s - 1 , j]+ sum((lambda[j]*f[r + 1]+ g[r + 1]-(s - r - mu[j])*f[r])*a[s - r , j], r = 1..s)	(Subscript[f, 0]+ 2*Subscript[\[Lambda], j])*s*Subscript[a, s , j] == (s - Subscript[\[Mu], j])*(s - 1 - Subscript[\[Mu], j])*Subscript[a, s - 1 , j]+ Sum[(Subscript[\[Lambda], j]*Subscript[f, r + 1]+ Subscript[g, r + 1]-(s - r - Subscript[\[Mu], j])*Subscript[f, r])*Subscript[a, s - r , j], {r, 1, s}, GenerateConditions->None]	Skipped - no semantic math	Skipped - no semantic math	-	-
2.7.E15	${\displaystyle{\displaystyle-\tfrac{3}{2}\pi+\delta\leq\operatorname{ph}\left((\lambda_{2}-\lambda_{1})z\right)}}$ -\tfrac{3}{2}\pi+\delta \leq \phase@{(\lambda_{2}-\lambda_{1})z}	${\displaystyle{\displaystyle j=1}}$	-(3)/(2)*Pi + delta <= argument((lambda[2]- lambda[1])*z)	-Divide[3,2]*Pi + \[Delta] <= Arg[(Subscript[\[Lambda], 2]- Subscript[\[Lambda], 1])*z]	Failure	Failure	Successful [Tested: 300]	Failed [300 / 300] Result: LessEqual[Complex[-3.846363576600251, 0.49999999999999994], 0.0] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: LessEqual[Complex[-3.846363576600251, 0.49999999999999994], -2.8797932657906435] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
2.7.E15	${\displaystyle{\displaystyle\operatorname{ph}\left((\lambda_{2}-\lambda_{1})z\right)\leq\tfrac{3}{2}\pi-\delta}}$ \phase@{(\lambda_{2}-\lambda_{1})z} \leq \tfrac{3}{2}\pi-\delta	${\displaystyle{\displaystyle j=1}}$	argument((lambda[2]- lambda[1])*z) <= (3)/(2)*Pi - delta	Arg[(Subscript[\[Lambda], 2]- Subscript[\[Lambda], 1])*z] <= Divide[3,2]*Pi - \[Delta]	Failure	Failure	Successful [Tested: 300]	Failed [300 / 300] Result: LessEqual[0.0, Complex[3.846363576600251, -0.49999999999999994]] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: LessEqual[-2.8797932657906435, Complex[3.846363576600251, -0.49999999999999994]] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
2.7.E16	${\displaystyle{\displaystyle-\tfrac{1}{2}\pi+\delta\leq\operatorname{ph}\left((\lambda_{2}-\lambda_{1})z\right)}}$ -\tfrac{1}{2}\pi+\delta \leq \phase@{(\lambda_{2}-\lambda_{1})z}	${\displaystyle{\displaystyle j=2}}$	-(1)/(2)*Pi + delta <= argument((lambda[2]- lambda[1])*z)	-Divide[1,2]*Pi + \[Delta] <= Arg[(Subscript[\[Lambda], 2]- Subscript[\[Lambda], 1])*z]	Failure	Failure	Successful [Tested: 300]	Failed [300 / 300] Result: LessEqual[Complex[-0.7047709230104579, 0.49999999999999994], 0.0] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: LessEqual[Complex[-0.7047709230104579, 0.49999999999999994], -2.8797932657906435] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
2.7.E16	${\displaystyle{\displaystyle\operatorname{ph}\left((\lambda_{2}-\lambda_{1})z\right)\leq\tfrac{5}{2}\pi-\delta}}$ \phase@{(\lambda_{2}-\lambda_{1})z} \leq \tfrac{5}{2}\pi-\delta	${\displaystyle{\displaystyle j=2}}$	argument((lambda[2]- lambda[1])*z) <= (5)/(2)*Pi - delta	Arg[(Subscript[\[Lambda], 2]- Subscript[\[Lambda], 1])*z] <= Divide[5,2]*Pi - \[Delta]	Failure	Failure	Successful [Tested: 300]	Failed [300 / 300] Result: LessEqual[0.0, Complex[6.987956230190044, -0.49999999999999994]] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: LessEqual[-2.8797932657906435, Complex[6.987956230190044, -0.49999999999999994]] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
2.7#Ex5	${\displaystyle{\displaystyle w_{1}(z)=e^{2\pi i\mu_{1}}w_{1}(ze^{-2\pi i})+C_{1}w_{2}(z)}}$ w_{1}(z) = e^{2\pi i\mu_{1}}w_{1}(ze^{-2\pi i})+C_{1}w_{2}(z)		w[1](z) = exp(2*Pi*I*mu[1])*w[1](z*exp(- 2*Pi*I))+ C[1]*w[2](z)	Subscript[w, 1][z] == Exp[2*Pi*I*Subscript[\[Mu], 1]]*Subscript[w, 1][z*Exp[- 2*Pi*I]]+ Subscript[C, 1]*Subscript[w, 2][z]	Skipped - no semantic math	Skipped - no semantic math	-	-
2.7#Ex6	${\displaystyle{\displaystyle w_{2}(z)=e^{-2\pi i\mu_{2}}w_{2}(ze^{2\pi i})+C_{2}w_{1}(z)}}$ w_{2}(z) = e^{-2\pi i\mu_{2}}w_{2}(ze^{2\pi i})+C_{2}w_{1}(z)		w[2](z) = exp(- 2*Pi*I*mu[2])*w[2](z*exp(2*Pi*I))+ C[2]*w[1](z)	Subscript[w, 2][z] == Exp[- 2*Pi*I*Subscript[\[Mu], 2]]*Subscript[w, 2][z*Exp[2*Pi*I]]+ Subscript[C, 2]*Subscript[w, 1][z]	Skipped - no semantic math	Skipped - no semantic math	-	-
2.7#Ex7	${\displaystyle{\displaystyle\Lambda_{1}=-ie^{(\mu_{2}-\mu_{1})\pi i}C_{1}/(2\pi)}}$ \Lambda_{1} = -ie^{(\mu_{2}-\mu_{1})\pi i}C_{1}/(2\pi)		Lambda[1] = - I*exp((mu[2]- mu[1])*Pi*I)*C[1]/(2*Pi)	Subscript[\[CapitalLambda], 1] == - I*Exp[(Subscript[\[Mu], 2]- Subscript[\[Mu], 1])*Pi*I]*Subscript[C, 1]/(2*Pi)	Skipped - no semantic math	Skipped - no semantic math	-	-
2.7#Ex8	${\displaystyle{\displaystyle\Lambda_{2}=iC_{2}/(2\pi)}}$ \Lambda_{2} = iC_{2}/(2\pi)		Lambda[2] = I*C[2]/(2*Pi)	Subscript[\[CapitalLambda], 2] == I*Subscript[C, 2]/(2*Pi)	Skipped - no semantic math	Skipped - no semantic math	-	-
2.7#Ex9	${\displaystyle{\displaystyle w=e^{-f_{0}z/2}W}}$ w = e^{-f_{0}z/2}W		w = exp(- f[0]*z/2)*W	w == Exp[- Subscript[f, 0]*z/2]*W	Skipped - no semantic math	Skipped - no semantic math	-	-
2.7#Ex10	${\displaystyle{\displaystyle t=z^{1/2}}}$ t = z^{1/2}		t = (z)^(1/2)	t == (z)^(1/2)	Skipped - no semantic math	Skipped - no semantic math	-	-
2.7.E21	${\displaystyle{\displaystyle w_{1}(x)=f^{-1/4}(x)\exp\left(\int f^{1/2}(x)\mathrm{d}x\right)\*\left(1+\epsilon_{1}(x)\right)}}$ w_{1}(x) = f^{-1/4}(x)\exp@{\int f^{1/2}(x)\diff{x}}\*\left(1+\epsilon_{1}(x)\right)		w[1](x) = (f(x)*)^(- 1/4)*exp(int((f(x))^(1/2), x))*(1 + epsilon[1](x))	Subscript[w, 1][x] == (f[x]*)^(- 1/4)*Exp[Integrate[(f[x])^(1/2), x, GenerateConditions->None]]*(1 + Subscript[\[Epsilon], 1][x])	Failure	Failure	Failed [300 / 300] Result: -8.260557290-4.173606164*I Test Values: {f = 1/2*3^(1/2)+1/2*I, x = 1.5, epsilon[1] = 1/2*3^(1/2)+1/2*I, w[1] = 1/2*3^(1/2)+1/2*I, epsilon = 1} Result: -8.260557290-4.173606164*I Test Values: {f = 1/2*3^(1/2)+1/2*I, x = 1.5, epsilon[1] = 1/2*3^(1/2)+1/2*I, w[1] = 1/2*3^(1/2)+1/2*I, epsilon = 2} Result: -8.260557290-4.173606164*I Test Values: {f = 1/2*3^(1/2)+1/2*I, x = 1.5, epsilon[1] = 1/2*3^(1/2)+1/2*I, w[1] = 1/2*3^(1/2)+1/2*I, epsilon = 3} Result: -10.30959540-3.624568058*I Test Values: {f = 1/2*3^(1/2)+1/2*I, x = 1.5, epsilon[1] = 1/2*3^(1/2)+1/2*I, w[1] = -1/2+1/2*I*3^(1/2), epsilon = 1} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-8.260557282600258, -4.173606160657738] Test Values: {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ϵ, 1], Rule[Subscript[w, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϵ, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-8.260557282600258, -4.173606160657738] Test Values: {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ϵ, 2], Rule[Subscript[w, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϵ, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
2.7.E22	${\displaystyle{\displaystyle w_{2}(x)=f^{-1/4}(x)\exp\left(-\int f^{1/2}(x)\mathrm{d}x\right)\*\left(1+\epsilon_{2}(x)\right)}}$ w_{2}(x) = f^{-1/4}(x)\exp@{-\int f^{1/2}(x)\diff{x}}\*\left(1+\epsilon_{2}(x)\right)		w[2](x) = (f(x)*)^(- 1/4)*exp(- int((f(x))^(1/2), x))*(1 + epsilon[2](x))	Subscript[w, 2][x] == (f[x]*)^(- 1/4)*Exp[- Integrate[(f[x])^(1/2), x, GenerateConditions->None]]*(1 + Subscript[\[Epsilon], 2][x])	Failure	Failure	Failed [300 / 300] Result: .82331014e-1+.8803583156*I Test Values: {f = 1/2*3^(1/2)+1/2*I, x = 1.5, epsilon[2] = 1/2*3^(1/2)+1/2*I, w[2] = 1/2*3^(1/2)+1/2*I, epsilon = 1} Result: .82331014e-1+.8803583156*I Test Values: {f = 1/2*3^(1/2)+1/2*I, x = 1.5, epsilon[2] = 1/2*3^(1/2)+1/2*I, w[2] = 1/2*3^(1/2)+1/2*I, epsilon = 2} Result: .82331014e-1+.8803583156*I Test Values: {f = 1/2*3^(1/2)+1/2*I, x = 1.5, epsilon[2] = 1/2*3^(1/2)+1/2*I, w[2] = 1/2*3^(1/2)+1/2*I, epsilon = 3} Result: -1.966707092+1.429396422*I Test Values: {f = 1/2*3^(1/2)+1/2*I, x = 1.5, epsilon[2] = 1/2*3^(1/2)+1/2*I, w[2] = -1/2+1/2*I*3^(1/2), epsilon = 1} ... skip entries to safe data	Failed [300 / 300] Result: Complex[0.08233101320006697, 0.8803583156922803] Test Values: {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ϵ, 1], Rule[Subscript[w, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϵ, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[0.08233101320006697, 0.8803583156922803] Test Values: {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ϵ, 2], Rule[Subscript[w, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϵ, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
2.7.E31	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}x}^{2}}=(x+\ln x)w}}$ \deriv[2]{w}{x} = (x+\ln@@{x})w	${\displaystyle{\displaystyle 0<x,x<\infty}}$	diff(w, [x$(2)]) = (x + ln(x))*w	D[w, {x, 2}] == (x + Log[x])*w	Failure	Failure	Failed [30 / 30] Result: -1.650181190-.9527325540*I Test Values: {w = 1/2*3^(1/2)+1/2*I, x = 1.5} Result: .1672703651+.9657359030e-1*I Test Values: {w = 1/2*3^(1/2)+1/2*I, x = .5} Result: -2.332333875-1.346573590*I Test Values: {w = 1/2*3^(1/2)+1/2*I, x = 2} Result: .9527325540-1.650181190*I Test Values: {w = -1/2+1/2*I*3^(1/2), x = 1.5} ... skip entries to safe data	Failed [30 / 30] Result: Complex[-1.6501811896465322, -0.9527325540540821] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5]} Result: Complex[0.1672703650342525, 0.09657359027997263] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 0.5]} ... skip entries to safe data
2.7.E35	${\displaystyle{\displaystyle\ifrac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}=w}}$ \ideriv[2]{w}{z} = w		diff(w, [z$(2)]) = w	D[w, {z, 2}] == w	Failure	Failure	Failed [70 / 70] Result: -.8660254040-.5000000000*I Test Values: {w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I} Result: -.8660254040-.5000000000*I Test Values: {w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)} Result: -.8660254040-.5000000000*I Test Values: {w = 1/2*3^(1/2)+1/2*I, z = 1/2-1/2*I*3^(1/2)} Result: -.8660254040-.5000000000*I Test Values: {w = 1/2*3^(1/2)+1/2*I, z = -1/2*3^(1/2)-1/2*I} ... skip entries to safe data	Failed [70 / 70] Result: Complex[-0.8660254037844387, -0.49999999999999994] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-0.8660254037844387, -0.49999999999999994] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
2.7.E36	${\displaystyle{\displaystyle w(z)=Aw_{1}(z)+Bw_{2}(z)}}$ w(z) = Aw_{1}(z)+Bw_{2}(z)		w(z) = Aw[1](z)+ Bw[2](z)	w[z] == Subscript[Aw, 1][z]+ Subscript[Bw, 2][z]	Skipped - no semantic math	Skipped - no semantic math	-	-
2.7.E37	${\displaystyle{\displaystyle w(z)=Cw_{3}(z)+Dw_{4}(z)}}$ w(z) = Cw_{3}(z)+Dw_{4}(z)		w(z) = Cw[3](z)+ Dw[4](z)	w[z] == Subscript[Cw, 3][z]+ Subscript[Dw, 4][z]	Skipped - no semantic math	Skipped - no semantic math	-	-