Mathieu Functions and Hill’s Equation - 28.8 Asymptotic Expansions for Large
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
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| 28.8#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \dfrac{\Mathieuce{m}@{x}{h^{2}}}{\Mathieuce{m}@{0}{h^{2}}} = \dfrac{2^{m-(\ifrac{1}{2})}}{\sigma_{m}}\left(W_{m}^{+}(x)(P_{m}(x)-Q_{m}(x))+W_{m}^{-}(x)(P_{m}(x)+Q_{m}(x))\right)}
\dfrac{\Mathieuce{m}@{x}{h^{2}}}{\Mathieuce{m}@{0}{h^{2}}} = \dfrac{2^{m-(\ifrac{1}{2})}}{\sigma_{m}}\left(W_{m}^{+}(x)(P_{m}(x)-Q_{m}(x))+W_{m}^{-}(x)(P_{m}(x)+Q_{m}(x))\right) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (MathieuCE(m, (h)^(2), x))/(MathieuCE(m, (h)^(2), 0)) = ((2)^(m -((1)/(2))))/(sigma[m])*((W[m])^(+)(x)*(P[m](x)- Q[m](x))+ (W[m])^(-)(x)*(P[m](x)+ Q[m](x)))
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Divide[MathieuC[m, (h)^(2), x],MathieuC[m, (h)^(2), 0]] == Divide[(2)^(m -(Divide[1,2])),Subscript[\[Sigma], m]]*((Subscript[W, m])^(+)[x]*(Subscript[P, m][x]- Subscript[Q, m][x])+ (Subscript[W, m])^(-)[x]*(Subscript[P, m][x]+ Subscript[Q, m][x]))
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Error | Failure | - | Skipped - Because timed out |
| 28.8#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \dfrac{\Mathieuse{m+1}@{x}{h^{2}}}{\Mathieuse{m+1}'@{0}{h^{2}}} = \dfrac{2^{m-(\ifrac{1}{2})}}{\tau_{m+1}}\left(W_{m}^{+}(x)(P_{m}(x)-Q_{m}(x))-W_{m}^{-}(x)(P_{m}(x)+Q_{m}(x))\right)}
\dfrac{\Mathieuse{m+1}@{x}{h^{2}}}{\Mathieuse{m+1}'@{0}{h^{2}}} = \dfrac{2^{m-(\ifrac{1}{2})}}{\tau_{m+1}}\left(W_{m}^{+}(x)(P_{m}(x)-Q_{m}(x))-W_{m}^{-}(x)(P_{m}(x)+Q_{m}(x))\right) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (MathieuSE(m + 1, (h)^(2), x))/(subs( temp=0, diff( MathieuSE(m + 1, (h)^(2), temp), temp$(1) ) )) = ((2)^(m -((1)/(2))))/(tau[m + 1])*((W[m])^(+)(x)*(P[m](x)- Q[m](x))- (W[m])^(-)(x)*(P[m](x)+ Q[m](x)))
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Divide[MathieuS[m + 1, (h)^(2), x],D[MathieuS[m + 1, (h)^(2), temp], {temp, 1}]/.temp-> 0] == Divide[(2)^(m -(Divide[1,2])),Subscript[\[Tau], m + 1]]*((Subscript[W, m])^(+)[x]*(Subscript[P, m][x]- Subscript[Q, m][x])- (Subscript[W, m])^(-)[x]*(Subscript[P, m][x]+ Subscript[Q, m][x]))
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Error | Failure | - | Skipped - Because timed out |