Mathieu Functions and Hill’s Equation - 28.6 Expansions for Small
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
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| 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)
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Subscript[, n -> Infinity]*Divide[(Subscript[\[Rho], n])^(j),(n)^(2)] >= k*Sqrt[1 - (k)^(2)]*(EllipticK[(k)^2])^(2)
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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
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k*Sqrt[1 - (k)^(2)]*(EllipticK[(k)^2])^(2) == 2.041834
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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 |