Mathieu Functions and Hill’s Equation - 28.6 Expansions for Small

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
28.6.E20	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \liminf_{n\to\infty}\frac{\rho_{n}^{(j)}}{n^{2}} \geq kk^{\prime}(\compellintKk@{k})^{2}} \liminf_{n\to\infty}\frac{\rho_{n}^{(j)}}{n^{2}} \geq kk^{\prime}(\compellintKk@{k})^{2}	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	[n = infinity]*((rho[n])^(j))/((n)^(2)) >= k*sqrt(1 - (k)^(2))*(EllipticK(k))^(2)	Subscript[, n -> Infinity]*Divide[(Subscript[\[Rho], n])^(j),(n)^(2)] >= k*Sqrt[1 - (k)^(2)]*(EllipticK[(k)^2])^(2)	Failure	Failure	Error	Failed [300 / 300] Result: GreaterEqual[Complex[0.5000000000000001, 0.8660254037844386], Indeterminate] Test Values: {Rule[j, 1], Rule[k, 1], Rule[n, 1], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ρ, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: GreaterEqual[Complex[0.12500000000000003, 0.21650635094610965], Indeterminate] Test Values: {Rule[j, 1], Rule[k, 1], Rule[n, 2], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ρ, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
28.6.E20	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle kk^{\prime}(\compellintKk@{k})^{2} = 2.04183\;4\dots} kk^{\prime}(\compellintKk@{k})^{2} = 2.04183\;4\dots	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	k*sqrt(1 - (k)^(2))*(EllipticK(k))^(2) = 2.041834	k*Sqrt[1 - (k)^(2)]*(EllipticK[(k)^2])^(2) == 2.041834	Failure	Failure	Error	Failed [3 / 3] Result: Indeterminate Test Values: {Rule[k, 1]} Result: Complex[4.25477173820126, -1.5664714954570549] Test Values: {Rule[k, 2]} ... skip entries to safe data