Bessel Functions - 10.37 Inequalities; Monotonicity

From testwiki
Jump to navigation Jump to search


DLMF Formula Constraints Maple Mathematica Symbolic
Maple
Symbolic
Mathematica
Numeric
Maple
Numeric
Mathematica
10.37.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\modBesselK{\nu}@{z}| < |\modBesselK{\mu}@{z}|}
|\modBesselK{\nu}@{z}| < |\modBesselK{\mu}@{z}|
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
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