10.21

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
10.21#Ex5	${\displaystyle{\displaystyle\rho_{\nu}(0)=0}}$ \rho_{\nu}(0) = 0		rho[nu](0) = 0	Subscript[\[Rho], \[Nu]][0] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
10.21.E11	${\displaystyle{\displaystyle 2\rho_{\nu}^{2}\frac{\mathrm{d}\rho_{\nu}}{\mathrm{d}t}\frac{{\mathrm{d}}^{3}\rho_{\nu}}{{\mathrm{d}t}^{3}}-3\rho_{\nu}^{2}\*\left(\frac{{\mathrm{d}}^{2}\rho_{\nu}}{{\mathrm{d}t}^{2}}\right)^{2}-4\pi^{2}\rho_{\nu}^{2}\*\left(\frac{\mathrm{d}\rho_{\nu}}{\mathrm{d}t}\right)^{2}+(4\rho_{\nu}^{2}+1-4\nu^{2})\left(\frac{\mathrm{d}\rho_{\nu}}{\mathrm{d}t}\right)^{4}=0}}$ 2\rho_{\nu}^{2}\deriv{\rho_{\nu}}{t}\deriv[3]{\rho_{\nu}}{t}-3\rho_{\nu}^{2}\*\left(\deriv[2]{\rho_{\nu}}{t}\right)^{2}-4\pi^{2}\rho_{\nu}^{2}\*\left(\deriv{\rho_{\nu}}{t}\right)^{2}+(4\rho_{\nu}^{2}+1-4\nu^{2})\left(\deriv{\rho_{\nu}}{t}\right)^{4} = 0		2*(rho[nu])^(2)*diff(rho[nu], t)*diff(rho[nu], [t$(3)])- 3*(rho[nu])^(2)*(diff(rho[nu], [t$(2)]))^(2)- 4*(Pi)^(2)* (rho[nu])^(2)*(diff(rho[nu], t))^(2)+(4*(rho[nu])^(2)+ 1 - 4*(nu)^(2))*(diff(rho[nu], t))^(4) = 0	2*(Subscript[\[Rho], \[Nu]])^(2)*D[Subscript[\[Rho], \[Nu]], t]*D[Subscript[\[Rho], \[Nu]], {t, 3}]- 3*(Subscript[\[Rho], \[Nu]])^(2)*(D[Subscript[\[Rho], \[Nu]], {t, 2}])^(2)- 4*(Pi)^(2)* (Subscript[\[Rho], \[Nu]])^(2)*(D[Subscript[\[Rho], \[Nu]], t])^(2)+(4*(Subscript[\[Rho], \[Nu]])^(2)+ 1 - 4*\[Nu]^(2))*(D[Subscript[\[Rho], \[Nu]], t])^(4) == 0	Successful	Successful	-	Successful [Tested: 300]
10.21.E17	${\displaystyle{\displaystyle\frac{\mathrm{d}c}{\mathrm{d}\nu}=2c\int_{0}^{\infty}K_{0}\left(2c\sinh t\right)e^{-2\nu t}\mathrm{d}t}}$ \deriv{c}{\nu} = 2c\int_{0}^{\infty}\modBesselK{0}@{2c\sinh@@{t}}e^{-2\nu t}\diff{t}		diff(c, nu) = 2*c*int(BesselK(0, 2*c*sinh(t))*exp(- 2*nu*t), t = 0..infinity)	D[c, \[Nu]] == 2*c*Integrate[BesselK[0, 2*c*Sinh[t]]*Exp[- 2*\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
10.21#Ex19	${\displaystyle{\displaystyle\alpha_{0}=1}}$ \alpha_{0} = 1		alpha[0] = 1	Subscript[\[Alpha], 0] == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
10.21#Ex20	${\displaystyle{\displaystyle\alpha_{1}=\alpha}}$ \alpha_{1} = \alpha		alpha[1] = alpha	Subscript[\[Alpha], 1] == \[Alpha]	Skipped - no semantic math	Skipped - no semantic math	-	-
10.21#Ex21	${\displaystyle{\displaystyle\alpha_{2}=\tfrac{3}{10}\alpha^{2}}}$ \alpha_{2} = \tfrac{3}{10}\alpha^{2}		alpha[2] = (3)/(10)*(alpha)^(2)	Subscript[\[Alpha], 2] == Divide[3,10]*\[Alpha]^(2)	Skipped - no semantic math	Skipped - no semantic math	-	-
10.21#Ex22	${\displaystyle{\displaystyle\alpha_{3}=-\tfrac{1}{350}\alpha^{3}+\tfrac{1}{70}}}$ \alpha_{3} = -\tfrac{1}{350}\alpha^{3}+\tfrac{1}{70}		alpha[3] = -(1)/(350)*(alpha)^(3)+(1)/(70)	Subscript[\[Alpha], 3] == -Divide[1,350]*\[Alpha]^(3)+Divide[1,70]	Skipped - no semantic math	Skipped - no semantic math	-	-
10.21#Ex23	${\displaystyle{\displaystyle\alpha_{4}=-\tfrac{479}{63000}\alpha^{4}-\tfrac{1}{3150}\alpha}}$ \alpha_{4} = -\tfrac{479}{63000}\alpha^{4}-\tfrac{1}{3150}\alpha		alpha[4] = -(479)/(63000)*(alpha)^(4)-(1)/(3150)*alpha	Subscript[\[Alpha], 4] == -Divide[479,63000]*\[Alpha]^(4)-Divide[1,3150]*\[Alpha]	Skipped - no semantic math	Skipped - no semantic math	-	-
10.21#Ex24	${\displaystyle{\displaystyle\alpha_{5}=\tfrac{20231}{80\;85000}\alpha^{5}-\tfrac{551}{1\;61700}\alpha^{2}}}$ \alpha_{5} = \tfrac{20231}{80\;85000}\alpha^{5}-\tfrac{551}{1\;61700}\alpha^{2}		alpha[5] = (20231)/(8085000)*(alpha)^(5)-(551)/(161700)*(alpha)^(2)	Subscript[\[Alpha], 5] == Divide[20231,8085000]*\[Alpha]^(5)-Divide[551,161700]*\[Alpha]^(2)	Skipped - no semantic math	Skipped - no semantic math	-	-
10.21.E46	${\displaystyle{\displaystyle a=\tfrac{1}{2}\ln 3}}$ a = \tfrac{1}{2}\ln@@{3}		a = (1)/(2)*ln(3)	a == Divide[1,2]*Log[3]	Failure	Failure	Failed [6 / 6] Result: -2.049306144 Test Values: {a = -3/2} Result: .9506938555 Test Values: {a = 3/2} ... skip entries to safe data	Failed [6 / 6] Result: -2.049306144334055 Test Values: {Rule[a, -1.5]} Result: 0.9506938556659451 Test Values: {Rule[a, 1.5]} ... skip entries to safe data
10.21.E46	${\displaystyle{\displaystyle\tfrac{1}{2}\ln 3=0.54931\ldots}}$ \tfrac{1}{2}\ln@@{3} = 0.54931\dotsc		(1)/(2)*ln(3) = 0.54931 ..	Divide[1,2]*Log[3] == 0.54931 \[Ellipsis]	Error	Failure	Skip - symbolical successful subtest	Failed [1 / 1] Result: Plus[0.5493061443340549, Times[-0.54931, …]] Test Values: {}
10.21#Ex51	${\displaystyle{\displaystyle\alpha=\frac{(m-1)\pi}{\lambda-1}}}$ \alpha = \frac{(m-1)\pi}{\lambda-1}		alpha = ((m - 1)*Pi)/(lambda - 1)	\[Alpha] == Divide[(m - 1)*Pi,\[Lambda]- 1]	Skipped - no semantic math	Skipped - no semantic math	-	-
10.21#Ex52	${\displaystyle{\displaystyle p=\frac{\mu+3}{8\lambda}}}$ p = \frac{\mu+3}{8\lambda}		p = (mu + 3)/(8*lambda)	p == Divide[\[Mu]+ 3,8*\[Lambda]]	Skipped - no semantic math	Skipped - no semantic math	-	-
10.21#Ex53	${\displaystyle{\displaystyle q=\frac{(\mu^{2}+46\mu-63)(\lambda^{3}-1)}{6(4\lambda)^{3}(\lambda-1)}}}$ q = \frac{(\mu^{2}+46\mu-63)(\lambda^{3}-1)}{6(4\lambda)^{3}(\lambda-1)}		q = (((mu)^(2)+ 46*mu - 63)*((lambda)^(3)- 1))/(6*(4*lambda)^(3)*(lambda - 1))	q == Divide[(\[Mu]^(2)+ 46*\[Mu]- 63)*(\[Lambda]^(3)- 1),6*(4*\[Lambda])^(3)*(\[Lambda]- 1)]	Skipped - no semantic math	Skipped - no semantic math	-	-
10.21#Ex54	${\displaystyle{\displaystyle r=\frac{(\mu^{3}+185\mu^{2}-2053\mu+1899)(\lambda^{5}-1)}{5(4\lambda)^{5}(\lambda-1)}}}$ r = \frac{(\mu^{3}+185\mu^{2}-2053\mu+1899)(\lambda^{5}-1)}{5(4\lambda)^{5}(\lambda-1)}		(((mu - 1)*((mu)^(2)- 114*mu + 1073)*((lambda)^(5)- 1))/(5*(4*lambda)^(5)*(lambda - 1))) = (((mu)^(3)+ 185*(mu)^(2)- 2053*mu + 1899)*((lambda)^(5)- 1))/(5*(4*lambda)^(5)*(lambda - 1))	(Divide[(\[Mu]- 1)*(\[Mu]^(2)- 114*\[Mu]+ 1073)*(\[Lambda]^(5)- 1),5*(4*\[Lambda])^(5)*(\[Lambda]- 1)]) == Divide[(\[Mu]^(3)+ 185*\[Mu]^(2)- 2053*\[Mu]+ 1899)*(\[Lambda]^(5)- 1),5*(4*\[Lambda])^(5)*(\[Lambda]- 1)]	Skipped - no semantic math	Skipped - no semantic math	-	-
10.21#Ex55	${\displaystyle{\displaystyle\alpha=\frac{(m-\tfrac{1}{2})\pi}{\lambda-1}}}$ \alpha = \frac{(m-\tfrac{1}{2})\pi}{\lambda-1}		alpha = ((m -(1)/(2))*Pi)/(lambda - 1)	\[Alpha] == Divide[(m -Divide[1,2])*Pi,\[Lambda]- 1]	Skipped - no semantic math	Skipped - no semantic math	-	-
10.21#Ex56	${\displaystyle{\displaystyle p=\frac{(\mu+3)\lambda-(\mu-1)}{8\lambda(\lambda-1)}}}$ p = \frac{(\mu+3)\lambda-(\mu-1)}{8\lambda(\lambda-1)}		p = ((mu + 3)*lambda -(mu - 1))/(8*lambda*(lambda - 1))	p == Divide[(\[Mu]+ 3)*\[Lambda]-(\[Mu]- 1),8*\[Lambda]*(\[Lambda]- 1)]	Skipped - no semantic math	Skipped - no semantic math	-	-
10.21#Ex57	${\displaystyle{\displaystyle q=\frac{(\mu^{2}+46\mu-63)\lambda^{3}-(\mu-1)(\mu-25)}{6(4\lambda)^{3}(\lambda-1)}}}$ q = \frac{(\mu^{2}+46\mu-63)\lambda^{3}-(\mu-1)(\mu-25)}{6(4\lambda)^{3}(\lambda-1)}		q = (((mu)^(2)+ 46*mu - 63)*(lambda)^(3)-(mu - 1)*(mu - 25))/(6*(4*lambda)^(3)*(lambda - 1))	q == Divide[(\[Mu]^(2)+ 46*\[Mu]- 63)*\[Lambda]^(3)-(\[Mu]- 1)*(\[Mu]- 25),6*(4*\[Lambda])^(3)*(\[Lambda]- 1)]	Skipped - no semantic math	Skipped - no semantic math	-	-
10.21#Ex58	${\displaystyle{\displaystyle r=\frac{(\mu^{3}+185\mu^{2}-2053\mu+1899)\lambda^{5}-(\mu-1)(\mu^{2}-114\mu+1073)}{5(4\lambda)^{5}(\lambda-1)}}}$ r = \frac{(\mu^{3}+185\mu^{2}-2053\mu+1899)\lambda^{5}-(\mu-1)(\mu^{2}-114\mu+1073)}{5(4\lambda)^{5}(\lambda-1)}		(((mu - 1)*((mu)^(2)- 114*mu + 1073)*((lambda)^(5)- 1))/(5*(4*lambda)^(5)*(lambda - 1))) = (((mu)^(3)+ 185*(mu)^(2)- 2053*mu + 1899)*(lambda)^(5)-(mu - 1)*((mu)^(2)- 114*mu + 1073))/(5*(4*lambda)^(5)*(lambda - 1))	(Divide[(\[Mu]- 1)*(\[Mu]^(2)- 114*\[Mu]+ 1073)*(\[Lambda]^(5)- 1),5*(4*\[Lambda])^(5)*(\[Lambda]- 1)]) == Divide[(\[Mu]^(3)+ 185*\[Mu]^(2)- 2053*\[Mu]+ 1899)*\[Lambda]^(5)-(\[Mu]- 1)*(\[Mu]^(2)- 114*\[Mu]+ 1073),5*(4*\[Lambda])^(5)*(\[Lambda]- 1)]	Skipped - no semantic math	Skipped - no semantic math	-	-