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
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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
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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)
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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)
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a == Divide[1,2]*Log[3]
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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 | - | - |