Bessel Functions - 10.18 Modulus and Phase Functions

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
10.18#Ex7	${\displaystyle{\displaystyle M_{\nu}\left(x\right)=\left({J_{\nu}^{2}}\left(x\right)+{Y_{\nu}^{2}}\left(x\right)\right)^{\frac{1}{2}}}}$ \HankelmodM{\nu}@{x} = \left(\BesselJ{\nu}^{2}@{x}+\BesselY{\nu}^{2}@{x}\right)^{\frac{1}{2}}	${\displaystyle{\displaystyle\Re(\nu+k+1)>0,\Re((-\nu)+k+1)>0}}$	Error	Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2] == ((BesselJ[\[Nu], x])^(2)+ (BesselY[\[Nu], x])^(2))^(Divide[1,2])	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	${\displaystyle{\displaystyle N_{\nu}\left(x\right)=\left({J_{\nu}'^{2}}\left(x\right)+{Y_{\nu}'^{2}}\left(x\right)\right)^{\frac{1}{2}}}}$ \HankelmodderivN{\nu}@{x} = \left(\BesselJ{\nu}'^{2}@{x}+\BesselY{\nu}'^{2}@{x}\right)^{\frac{1}{2}}		Error	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])	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	${\displaystyle{\displaystyle(x^{2}-\nu^{2})M_{\nu}\left(x\right)M_{\nu}'\left(x\right)+x^{2}N_{\nu}\left(x\right)N_{\nu}'\left(x\right)+x{N_{\nu}^{2}}\left(x\right)=0}}$ (x^{2}-\nu^{2})\HankelmodM{\nu}@{x}\HankelmodM{\nu}'@{x}+x^{2}\HankelmodderivN{\nu}@{x}\HankelmodderivN{\nu}'@{x}+x\HankelmodderivN{\nu}^{2}@{x} = 0		Error	((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	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	${\displaystyle{\displaystyle x^{2}M_{\nu}''\left(x\right)+xM_{\nu}'\left(x\right)+(x^{2}-\nu^{2})M_{\nu}\left(x\right)=\frac{4}{\pi^{2}{{M_{\nu}^{3}}(x)}}}}$ x^{2}\HankelmodM{\nu}''@{x}+x\HankelmodM{\nu}'@{x}+(x^{2}-\nu^{2})\HankelmodM{\nu}@{x} = \frac{4}{\pi^{2}{\HankelmodM{\nu}^{3}(x)}}		Error	(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)]	Missing Macro Error	Translation Error	-	-