Bessel Functions - 10.18 Modulus and Phase Functions
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
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| 10.18#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelmodM{\nu}@{x} = \left(\BesselJ{\nu}^{2}@{x}+\BesselY{\nu}^{2}@{x}\right)^{\frac{1}{2}}}
\HankelmodM{\nu}@{x} = \left(\BesselJ{\nu}^{2}@{x}+\BesselY{\nu}^{2}@{x}\right)^{\frac{1}{2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(\nu+k+1)} > 0, \realpart@@{((-\nu)+k+1)} > 0} | Error
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Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2] == ((BesselJ[\[Nu], x])^(2)+ (BesselY[\[Nu], x])^(2))^(Divide[1,2])
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Missing Macro Error | Failure | - | Failed [30 / 30]
Result: Complex[0.19554332981034928, -0.3390785475644471]
Test Values: {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Complex[0.7197518351343698, 1.0182547128018542]
Test Values: {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
... skip entries to safe data |
| 10.18#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelmodderivN{\nu}@{x} = \left(\BesselJ{\nu}'^{2}@{x}+\BesselY{\nu}'^{2}@{x}\right)^{\frac{1}{2}}}
\HankelmodderivN{\nu}@{x} = \left(\BesselJ{\nu}'^{2}@{x}+\BesselY{\nu}'^{2}@{x}\right)^{\frac{1}{2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
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Sqrt[KelvinKer[\[Nu], x]^2 + KelvinKei[\[Nu], x]^2] == ((D[BesselJ[\[Nu], x], {x, 1}])^(2)+ (D[BesselY[\[Nu], x], {x, 1}])^(2))^(Divide[1,2])
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Missing Macro Error | Failure | - | Failed [30 / 30]
Result: Complex[-0.3065654786420606, 0.09106250304027241]
Test Values: {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Complex[-0.41179972752410343, -0.08651542233456301]
Test Values: {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
... skip entries to safe data |
| 10.18.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (x^{2}-\nu^{2})\HankelmodM{\nu}@{x}\HankelmodM{\nu}'@{x}+x^{2}\HankelmodderivN{\nu}@{x}\HankelmodderivN{\nu}'@{x}+x\HankelmodderivN{\nu}^{2}@{x} = 0}
(x^{2}-\nu^{2})\HankelmodM{\nu}@{x}\HankelmodM{\nu}'@{x}+x^{2}\HankelmodderivN{\nu}@{x}\HankelmodderivN{\nu}'@{x}+x\HankelmodderivN{\nu}^{2}@{x} = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
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((x)^(2)- \[Nu]^(2))*Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2]*D[Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2], {x, 1}]+ (x)^(2)* Sqrt[KelvinKer[\[Nu], x]^2 + KelvinKei[\[Nu], x]^2]*D[Sqrt[KelvinKer[\[Nu], x]^2 + KelvinKei[\[Nu], x]^2], {x, 1}]+ x*(Sqrt[KelvinKer[\[Nu], x]^2 + KelvinKei[\[Nu], x]^2])^(2) == 0
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Missing Macro Error | Aborted | - | Failed [30 / 30]
Result: Complex[0.7620133104065328, -0.7345190431210711]
Test Values: {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Complex[-3.2607567755462643, -4.475082123070706]
Test Values: {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
... skip entries to safe data |
| 10.18.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x^{2}\HankelmodM{\nu}''@{x}+x\HankelmodM{\nu}'@{x}+(x^{2}-\nu^{2})\HankelmodM{\nu}@{x} = \frac{4}{\pi^{2}{\HankelmodM{\nu}^{3}(x)}}}
x^{2}\HankelmodM{\nu}''@{x}+x\HankelmodM{\nu}'@{x}+(x^{2}-\nu^{2})\HankelmodM{\nu}@{x} = \frac{4}{\pi^{2}{\HankelmodM{\nu}^{3}(x)}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
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(x)^(2)* D[Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2], {x, 2}]+ x*D[Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2], {x, 1}]+((x)^(2)- \[Nu]^(2))*Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2] == Divide[4,(Pi)^(2)*(Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2])^(3)]
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Missing Macro Error | Translation Error | - | - |