Mathieu Functions and Hill’s Equation - 28.26 Asymptotic Approximations for Large

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
28.26.E3	${\displaystyle{\displaystyle\phi=2h\sinh z-\left(m+\tfrac{1}{2}\right)\operatorname{arctan}\left(\sinh z\right)}}$ \phi = 2h\sinh@@{z}-\left(m+\tfrac{1}{2}\right)\atan@{\sinh@@{z}}		phi = 2*h*sinh(z)-(m +(1)/(2))*arctan(sinh(z))	\[Phi] == 2*h*Sinh[z]-(m +Divide[1,2])*ArcTan[Sinh[z]]	Failure	Failure	Failed [300 / 300] Result: 1.309060595-.9846819085*I Test Values: {h = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1} Result: 2.148731429-.6275515075*I Test Values: {h = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[1.3090605953108105, -0.9846819068983852] Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[2.1487314296378672, -0.6275515058300114] Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data