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)	Error	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)	Error	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))	Divide[(2)^\[ScriptL]* (\[ScriptL])!,(2*\[ScriptL]+ 1)!] == Divide[1,(2*\[ScriptL]+ 1)!!]	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: {}