Mathieu Functions and Hill’s Equation - 28.7 Analytic Continuation of Eigenvalues
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 28.7.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}\left(\Mathieueigvala{2n}@{q}-(2n)^{2}\right) = 0}
\sum_{n=0}^{\infty}\left(\Mathieueigvala{2n}@{q}-(2n)^{2}\right) = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sum(MathieuA(2*n, q)-(2*n)^(2), n = 0..infinity) = 0
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Sum[MathieuCharacteristicA[2*n, q]-(2*n)^(2), {n, 0, Infinity}, GenerateConditions->None] == 0
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Failure | Failure | Skipped - Because timed out | Skipped - Because timed out |
| 28.7.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}\left(\Mathieueigvala{2n+1}@{q}-(2n+1)^{2}\right) = q}
\sum_{n=0}^{\infty}\left(\Mathieueigvala{2n+1}@{q}-(2n+1)^{2}\right) = q |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sum(MathieuA(2*n + 1, q)-(2*n + 1)^(2), n = 0..infinity) = q
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Sum[MathieuCharacteristicA[2*n + 1, q]-(2*n + 1)^(2), {n, 0, Infinity}, GenerateConditions->None] == q
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Failure | Failure | Skipped - Because timed out | Skipped - Because timed out |
| 28.7.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}\left(\Mathieueigvalb{2n+1}@{q}-(2n+1)^{2}\right) = -q}
\sum_{n=0}^{\infty}\left(\Mathieueigvalb{2n+1}@{q}-(2n+1)^{2}\right) = -q |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sum(MathieuB(2*n + 1, q)-(2*n + 1)^(2), n = 0..infinity) = - q
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Sum[MathieuCharacteristicB[2*n + 1, q]-(2*n + 1)^(2), {n, 0, Infinity}, GenerateConditions->None] == - q
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Failure | Failure | Skipped - Because timed out | Skipped - Because timed out |
| 28.7.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}\left(\Mathieueigvalb{2n+2}@{q}-(2n+2)^{2}\right) = 0}
\sum_{n=0}^{\infty}\left(\Mathieueigvalb{2n+2}@{q}-(2n+2)^{2}\right) = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sum(MathieuB(2*n + 2, q)-(2*n + 2)^(2), n = 0..infinity) = 0
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Sum[MathieuCharacteristicB[2*n + 2, q]-(2*n + 2)^(2), {n, 0, Infinity}, GenerateConditions->None] == 0
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Failure | Failure | Skipped - Because timed out | Skipped - Because timed out |