Bessel Functions - 10.21 Zeros

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DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
10.21#Ex5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \rho_{\nu}(0) = 0}
\rho_{\nu}(0) = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
rho[nu](0) = 0
 
Subscript[\[Rho], \[Nu]][0] == 0
 Skipped - no semantic math Skipped - no semantic math - -
10.21.E11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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}\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		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
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 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{c}{\nu} = 2c\int_{0}^{\infty}\modBesselK{0}@{2c\sinh@@{t}}e^{-2\nu t}\diff{t}}
\deriv{c}{\nu} = 2c\int_{0}^{\infty}\modBesselK{0}@{2c\sinh@@{t}}e^{-2\nu t}\diff{t}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
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 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{0} = 1}
\alpha_{0} = 1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
alpha[0] = 1
 
Subscript[\[Alpha], 0] == 1
 Skipped - no semantic math Skipped - no semantic math - -
10.21#Ex20 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{1} = \alpha}
\alpha_{1} = \alpha		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
alpha[1] = alpha
 
Subscript[\[Alpha], 1] == \[Alpha]
 Skipped - no semantic math Skipped - no semantic math - -
10.21#Ex21 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{2} = \tfrac{3}{10}\alpha^{2}}
\alpha_{2} = \tfrac{3}{10}\alpha^{2}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
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 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{3} = -\tfrac{1}{350}\alpha^{3}+\tfrac{1}{70}}
\alpha_{3} = -\tfrac{1}{350}\alpha^{3}+\tfrac{1}{70}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
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 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{4} = -\tfrac{479}{63000}\alpha^{4}-\tfrac{1}{3150}\alpha}
\alpha_{4} = -\tfrac{479}{63000}\alpha^{4}-\tfrac{1}{3150}\alpha		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
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 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
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 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a = \tfrac{1}{2}\ln@@{3}}
a = \tfrac{1}{2}\ln@@{3}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
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 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}\ln@@{3} = 0.54931\dotsc}
\tfrac{1}{2}\ln@@{3} = 0.54931\dotsc		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(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 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha = \frac{(m-1)\pi}{\lambda-1}}
\alpha = \frac{(m-1)\pi}{\lambda-1}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
alpha = ((m - 1)*Pi)/(lambda - 1)
 
\[Alpha] == Divide[(m - 1)*Pi,\[Lambda]- 1]
 Skipped - no semantic math Skipped - no semantic math - -
10.21#Ex52 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p = \frac{\mu+3}{8\lambda}}
p = \frac{\mu+3}{8\lambda}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
p = (mu + 3)/(8*lambda)
 
p == Divide[\[Mu]+ 3,8*\[Lambda]]
 Skipped - no semantic math Skipped - no semantic math - -
10.21#Ex53 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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)}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
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 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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)}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(((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 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha = \frac{(m-\tfrac{1}{2})\pi}{\lambda-1}}
\alpha = \frac{(m-\tfrac{1}{2})\pi}{\lambda-1}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
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 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p = \frac{(\mu+3)\lambda-(\mu-1)}{8\lambda(\lambda-1)}}
p = \frac{(\mu+3)\lambda-(\mu-1)}{8\lambda(\lambda-1)}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
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 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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)}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
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 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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)}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(((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 - -
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