Coulomb Functions - 33.5 Limiting Forms for Small , Small , or Large
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 33.5#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \regCoulombF{\ell}@{0}{\rho} = (\pi\rho/2)^{1/2}\BesselJ{\ell+\frac{1}{2}}@{\rho}}
\regCoulombF{\ell}@{0}{\rho} = (\pi\rho/2)^{1/2}\BesselJ{\ell+\frac{1}{2}}@{\rho} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{((\ell+\frac{1}{2})+k+1)} > 0} | CoulombF(ell, 0, rho) = (Pi*rho/2)^(1/2)* BesselJ(ell +(1)/(2), rho)
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Error
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Failure | Missing Macro Error | Error | - |
| 33.5#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \regCoulombF{0}@{0}{\rho} = \sin@@{\rho}}
\regCoulombF{0}@{0}{\rho} = \sin@@{\rho} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | CoulombF(0, 0, rho) = sin(rho)
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Error
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Successful | Missing Macro Error | - | - |
| 33.5.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2^{\ell}\ell!}{(2\ell+1)!} = \frac{1}{(2\ell+1)!!}}
\frac{2^{\ell}\ell!}{(2\ell+1)!} = \frac{1}{(2\ell+1)!!} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(\ell+1+\iunit\eta)} > 0} | ((2)^(ell)* factorial(ell))/(factorial(2*ell + 1)) = (1)/(doublefactorial(2*ell + 1))
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Divide[(2)^\[ScriptL]* (\[ScriptL])!,(2*\[ScriptL]+ 1)!] == Divide[1,(2*\[ScriptL]+ 1)!!]
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Failure | Failure | Error | Failed [1 / 1]
Result: Plus[Times[Power[2.0, ℓ], Factorial[ℓ], Power[Factorial[Plus[1.0, Times[2.0, ℓ]]], -1]], Times[-1.0, Power[Factorial2[Plus[1.0, Times[2.0, ℓ]]], -1]]]
Test Values: {}
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