36.7

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
36.7#Ex1	${\displaystyle{\displaystyle y_{m}=-\sqrt{2\pi(2m+1)}}}$ y_{m} = -\sqrt{2\pi(2m+1)}		y[m] = -sqrt(2*Pi*(2*m + 1))	Subscript[y, m] == -Sqrt[2*Pi*(2*m + 1)]	Skipped - no semantic math	Skipped - no semantic math	-	-
36.7#Ex2	${\displaystyle{\displaystyle x_{m,n}^{+}=\sqrt{\dfrac{2}{-y_{m}}}\left(2n+\tfrac{1}{2}+(-1)^{m}\tfrac{1}{2}+\tfrac{1}{4}\right)\pi}}$ x_{m,n}^{+} = \sqrt{\dfrac{2}{-y_{m}}}\left(2n+\tfrac{1}{2}+(-1)^{m}\tfrac{1}{2}+\tfrac{1}{4}\right)\pi		(x[m , n])^(+) = sqrt((2)/(- y[m]))*(2*n +(1)/(2)+(- 1)^(m)*(1)/(2)+(1)/(4))*Pi	(Subscript[x, m , n])^(+) == Sqrt[Divide[2,- Subscript[y, m]]]*(2*n +Divide[1,2]+(- 1)^(m)*Divide[1,2]+Divide[1,4])*Pi	Skipped - no semantic math	Skipped - no semantic math	-	-
36.7#Ex3	${\displaystyle{\displaystyle x_{n}=+\left(\dfrac{8}{27}\right)^{1/2}|y_{n}|^{3/2}(1+\xi_{n})}}$ x_{n} = +\left(\dfrac{8}{27}\right)^{1/2}|y_{n}|^{3/2}(1+\xi_{n})		x[n] = +((8)/(27))^(1/2)*(abs(y[n]))^(3/2)*(1 + xi[n])	Subscript[x, n] == +(Divide[8,27])^(1/2)*(Abs[Subscript[y, n]])^(3/2)*(1 + Subscript[\[Xi], n])	Skipped - no semantic math	Skipped - no semantic math	-	-
36.7#Ex4	${\displaystyle{\displaystyle y_{n}=-\left(\frac{3\pi(8n+5)}{9+8\xi_{n}}\right)^{1/2}}}$ y_{n} = -\left(\frac{3\pi(8n+5)}{9+8\xi_{n}}\right)^{1/2}		y[n] = -((3*Pi*(8*n + 5))/(9 + 8*xi[n]))^(1/2)	Subscript[y, n] == -(Divide[3*Pi*(8*n + 5),9 + 8*Subscript[\[Xi], n]])^(1/2)	Skipped - no semantic math	Skipped - no semantic math	-	-
36.7.E3	${\displaystyle{\displaystyle\frac{3\pi(8n+5)}{9+8\xi_{n}}\xi_{n}^{3/2}=\dfrac{27}{16}\left(\dfrac{3}{2}\right)^{1/2}\left(\ln\left(\frac{1}{\xi_{n}}\right)+3\ln\left(\dfrac{3}{2}\right)\right)}}$ \frac{3\pi(8n+5)}{9+8\xi_{n}}\xi_{n}^{3/2} = \dfrac{27}{16}\left(\dfrac{3}{2}\right)^{1/2}\left(\ln@{\frac{1}{\xi_{n}}}+3\ln@{\dfrac{3}{2}}\right)		(3*Pi*(8*n + 5))/(9 + 8*xi[n])*(xi[n])^(3/2) = (27)/(16)*((3)/(2))^(1/2)*(ln((1)/(xi[n]))+ 3*ln((3)/(2)))	Divide[3*Pi*(8*n + 5),9 + 8*Subscript[\[Xi], n]]*(Subscript[\[Xi], n])^(3/2) == Divide[27,16]*(Divide[3,2])^(1/2)*(Log[Divide[1,Subscript[\[Xi], n]]]+ 3*Log[Divide[3,2]])	Failure	Failure	Failed [300 / 300] Result: 3.887397376+4.913760852*I Test Values: {xi = 1/2*3^(1/2)+1/2*I, xi[n] = 1/2*3^(1/2)+1/2*I, n = 1} Result: 7.826714845+7.271674350*I Test Values: {xi = 1/2*3^(1/2)+1/2*I, xi[n] = 1/2*3^(1/2)+1/2*I, n = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[3.8873973728456934, 4.913760851775014] Test Values: {Rule[n, 1], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ξ, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[7.826714842534605, 7.271674348744825] Test Values: {Rule[n, 2], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ξ, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
36.7.E4	${\displaystyle{\displaystyle z_{n}=+3(\tfrac{1}{4}\pi(2n-\tfrac{1}{2}))^{1/3}\\ }}$ z_{n} = + 3(\tfrac{1}{4}\pi(2n-\tfrac{1}{2}))^{1/3}\\		z[n] = + 3*((1)/(4)*Pi*(2*n -(1)/(2)))^(1/3)	Subscript[z, n] == + 3*(Divide[1,4]*Pi*(2*n -Divide[1,2]))^(1/3)	Skipped - no semantic math	Skipped - no semantic math	-	-
36.7#Ex5	${\displaystyle{\displaystyle\Delta z=\frac{9\pi}{2z_{n}^{2}}}}$ \Delta z = \frac{9\pi}{2z_{n}^{2}}		Delta*z = (9*Pi)/(2*(z[n])^(2))	\[CapitalDelta]*z == Divide[9*Pi,2*(Subscript[z, n])^(2)]	Skipped - no semantic math	Skipped - no semantic math	-	-
36.7#Ex6	${\displaystyle{\displaystyle\Delta x=\frac{6\pi}{z_{n}}}}$ \Delta x = \frac{6\pi}{z_{n}}		Delta*x = (6*Pi)/(x + y*I[n])	\[CapitalDelta]*x == Divide[6*Pi,Subscript[x + y*I, n]]	Skipped - no semantic math	Skipped - no semantic math	-	-
36.7.E6	${\displaystyle{\displaystyle\exp\left(-2\pi i\left(\frac{z-z_{n}}{\Delta z}+\frac{2x}{\Delta x}\right)\right)\*{\left(2\exp\left(\frac{-6\pi ix}{\Delta x}\right)\cos\left(\frac{2\sqrt{3}\pi y}{\Delta x}\right)+1\right)}=\sqrt{3}}}$ \exp@{-2\pi i\left(\frac{z-z_{n}}{\Delta z}+\frac{2x}{\Delta x}\right)}\*{\left(2\exp@{\frac{-6\pi ix}{\Delta x}}\cos@{\frac{2\sqrt{3}\pi y}{\Delta x}}+1\right)} = \sqrt{3}		exp(- 2*Pi*I*(((x + y*I)-x + y*I[n])/(Delta*(x + y*I))+(2*x)/(Delta*x)))*(2*exp((- 6*Pi*I*x)/(Delta*x))*cos((2*sqrt(3)*Pi*y)/(Delta*x))+ 1) = sqrt(3)	Exp[- 2*Pi*I*(Divide[(x + y*I)-Subscript[x + y*I, n],\[CapitalDelta]*(x + y*I)]+Divide[2*x,\[CapitalDelta]*x])]*(2*Exp[Divide[- 6*Pi*I*x,\[CapitalDelta]*x]]*Cos[Divide[2*Sqrt[3]*Pi*y,\[CapitalDelta]*x]]+ 1) == Sqrt[3]	Failure	Failure	Error	Failed [300 / 300] Result: Plus[-1.7320508075688772, Times[Complex[1.0151974851172445, -0.010763380729874927], Power[2.718281828459045, Times[Complex[0.0, -6.283185307179586], Plus[Complex[1.7320508075688774, -0.9999999999999999], Times[Complex[0.4553418012614795, 0.12200846792814624], Plus[Complex[1.5, -1.5], Times[-1.0, Subscript[Complex[1.5, -1.5], 1]]]]]]]]] Test Values: {Rule[n, 1], Rule[x, 1.5], Rule[y, -1.5], Rule[Δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Plus[-1.7320508075688772, Times[Complex[1.0151974851172445, -0.010763380729874927], Power[2.718281828459045, Times[Complex[0.0, -6.283185307179586], Plus[Complex[1.7320508075688774, -0.9999999999999999], Times[Complex[0.4553418012614795, 0.12200846792814624], Plus[Complex[1.5, -1.5], Times[-1.0, Subscript[Complex[1.5, -1.5], 2]]]]]]]]] Test Values: {Rule[n, 2], Rule[x, 1.5], Rule[y, -1.5], Rule[Δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data