Bessel Functions - 10.45 Functions of Imaginary Order
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 10.45.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x^{2}\deriv[2]{w}{x}+x\deriv{w}{x}+(\nu^{2}-x^{2})w = 0}
x^{2}\deriv[2]{w}{x}+x\deriv{w}{x}+(\nu^{2}-x^{2})w = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (x)^(2)* diff(w, [x$(2)])+ x*diff(w, x)+((nu)^(2)- (x)^(2))*w = 0
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(x)^(2)* D[w, {x, 2}]+ x*D[w, x]+(\[Nu]^(2)- (x)^(2))*w == 0
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Failure | Failure | Failed [240 / 300] Result: -1.948557159-.1249999996*I
Test Values: {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, x = 3/2}
Result: -.2165063507+.8750000006*I
Test Values: {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, x = 1/2}
... skip entries to safe data |
Failed [240 / 300]
Result: Complex[-1.948557158514987, -0.12499999999999989]
Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Complex[-1.9485571585149875, -2.125]
Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
... skip entries to safe data |
| 10.45.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\modBesselIimag{\nu}@{x} = \realpart@{\modBesselI{i\nu}@{x}}}
\displaystyle\modBesselIimag{\nu}@{x} = \realpart@{\modBesselI{i\nu}@{x}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{((\iunit \nu)+k+1)} > 0} | Re(BesselI(I*(nu), x)) = Re(BesselI(I*nu, x))
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Re[BesselI[I*\[Nu], x]] == Re[BesselI[I*\[Nu], x]]
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Successful | Successful | - | Successful [Tested: 30] |
| 10.45.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\modBesselKimag{\nu}@{x} = \modBesselK{i\nu}@{x}}
\displaystyle\modBesselKimag{\nu}@{x} = \modBesselK{i\nu}@{x} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | BesselK(I*(nu), x) = BesselK(I*nu, x)
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BesselK[I*\[Nu], x] == BesselK[I*\[Nu], x]
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Successful | Successful | - | Successful [Tested: 30] |
| 10.45.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\modBesselIimag{-\nu}@{x} = \modBesselIimag{\nu}@{x}}
\displaystyle\modBesselIimag{-\nu}@{x} = \modBesselIimag{\nu}@{x} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Re(BesselI(I*(- nu), x)) = Re(BesselI(I*(nu), x)) |
Re[BesselI[I*- \[Nu], x]] == Re[BesselI[I*\[Nu], x]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.45.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\modBesselKimag{-\nu}@{x} = \modBesselKimag{\nu}@{x}}
\displaystyle\modBesselKimag{-\nu}@{x} = \modBesselKimag{\nu}@{x} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | BesselK(I*(- nu), x) = BesselK(I*(nu), x) |
BesselK[I*- \[Nu], x] == BesselK[I*\[Nu], x] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.45.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\modBesselKimag{\nu}@{x},\modBesselIimag{\nu}@{x}} = 1/x}
\Wronskian@{\modBesselKimag{\nu}@{x},\modBesselIimag{\nu}@{x}} = 1/x |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (BesselK(I*(nu), x))*diff(Re(BesselI(I*(nu), x)), x)-diff(BesselK(I*(nu), x), x)*(Re(BesselI(I*(nu), x))) = 1/x
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Wronskian[{BesselK[I*\[Nu], x], Re[BesselI[I*\[Nu], x]]}, x] == 1/x
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Failure | Failure | Error | Failed [30 / 30]
Result: Plus[-0.6666666666666666, Times[0.5, Plus[Complex[1.0700115379721733, -0.3754447148158467], Times[Complex[0.1636629185333998, 0.09141848176750039], Derivative[1][Re][Complex[2.445786867824693, 0.6492150843755028]]]]]]
Test Values: {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Plus[-0.6666666666666666, Times[0.5, Plus[Complex[0.8415452902387464, 0.2726729041814867], Times[Complex[0.3412924192180222, 0.19179892830603273], Derivative[1][Re][Complex[1.3137906770541619, -0.7251169608509622]]]]]]
Test Values: {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
... skip entries to safe data |
| 10.45.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselKimag{0}@{x} = \modBesselK{0}@{x}}
\modBesselKimag{0}@{x} = \modBesselK{0}@{x} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | BesselK(I*(0), x) = BesselK(0, x)
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BesselK[I*0, x] == BesselK[0, x]
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Successful | Successful | - | Successful [Tested: 3] |