Bessel Functions - 10.37 Inequalities; Monotonicity

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
10.37.E1	${\displaystyle{\displaystyle|K_{\nu}\left(z\right)|<|K_{\mu}\left(z\right)|}}$ |\modBesselK{\nu}@{z}| < |\modBesselK{\mu}@{z}|		abs(BesselK(nu, z)) < abs(BesselK(mu, z))	Abs[BesselK[\[Nu], z]] < Abs[BesselK[\[Mu], z]]	Failure	Failure	Failed [204 / 300] Result: .6496143723 < .6496143723 Test Values: {mu = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I} Result: 3.110500858 < 3.110500858 Test Values: {mu = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [184 / 300] Result: False Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: False Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]} ... skip entries to safe data