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http://functions.wolfram.com/01.03.26.0095.01
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E^(Sqrt[a] z) == (1/Sqrt[a]) (MathieuSPrime[a, 0, I z] +
I MathieuCPrime[a, 0, I z])
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Cell[BoxData[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[SqrtBox["a"], " ", "z"]]], "\[Equal]", RowBox[List[FractionBox["1", SqrtBox["a"]], RowBox[List["(", RowBox[List[RowBox[List["MathieuSPrime", "[", RowBox[List["a", ",", "0", ",", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["MathieuCPrime", "[", RowBox[List["a", ",", "0", ",", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]]]]]], ")"]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <msup> <mi> ⅇ </mi> <mrow> <msqrt> <mi> a </mi> </msqrt> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <msqrt> <mi> a </mi> </msqrt> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> Se </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mn> 0 </mn> <mo> , </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mtext> </mtext> <mrow> <msub> <mi> Ce </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mn> 0 </mn> <mo> , </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <apply> <ci> Subscript </ci> <ci> Se </ci> <ci> z </ci> </apply> <ci> a </ci> <cn type='integer'> 0 </cn> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> </apply> <apply> <times /> <imaginaryi /> <apply> <apply> <ci> Subscript </ci> <ci> Ce </ci> <ci> z </ci> </apply> <ci> a </ci> <cn type='integer'> 0 </cn> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox["\[ExponentialE]", RowBox[List[SqrtBox["a_"], " ", "z_"]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["MathieuSPrime", "[", RowBox[List["a", ",", "0", ",", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["MathieuCPrime", "[", RowBox[List["a", ",", "0", ",", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]]]]]], SqrtBox["a"]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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