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http://functions.wolfram.com/11.01.26.0001.01
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MathieuC[MathieuCharacteristicA[r, q], q, z] ==
Sqrt[Pi] Sqrt[Sin[z]] SpheroidalPS[r - 1/2, 1/2, 2 Sqrt[q], Cos[z]]
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Cell[BoxData[RowBox[List[RowBox[List["MathieuC", "[", RowBox[List[RowBox[List["MathieuCharacteristicA", "[", RowBox[List["r", ",", "q"]], "]"]], ",", "q", ",", "z"]], "]"]], "\[Equal]", RowBox[List[SqrtBox["\[Pi]"], " ", SqrtBox[RowBox[List["Sin", "[", "z", "]"]]], RowBox[List["SpheroidalPS", "[", RowBox[List[RowBox[List["r", "-", FractionBox["1", "2"]]], ",", FractionBox["1", "2"], ",", RowBox[List["2", SqrtBox["q"]]], ",", RowBox[List["Cos", "[", "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> <mrow> <mi> Ce </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msub> <semantics> <mi> a </mi> <annotation-xml encoding='MathML-Content'> <ci> MathieuCharacteristicA </ci> </annotation-xml> </semantics> <mi> r </mi> </msub> <mo> ( </mo> <mi> q </mi> <mo> ) </mo> </mrow> <mo> , </mo> <mi> q </mi> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <msqrt> <mi> π </mi> </msqrt> <mo> ⁢ </mo> <msqrt> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </msqrt> <mo> ⁢ </mo> <semantics> <mrow> <msub> <mi> PS </mi> <mrow> <mrow> <mi> r </mi> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </msub> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mi> q </mi> </msqrt> </mrow> <mo> , </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubscriptBox[StyleBox["PS", "IT"], RowBox[List[TagBox[RowBox[List["r", "-", FractionBox["1", "2"]]], SpheroidalPS, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "2"], SpheroidalPS, Rule[Editable, True], Rule[Selectable, True]]]]], "(", RowBox[List[TagBox[RowBox[List["2", " ", SqrtBox["q"]]], SpheroidalPS, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["cos", "(", "z", ")"]], SpheroidalPS, Rule[Editable, True], Rule[Selectable, True]]]], ")"]], InterpretTemplate[Function[SpheroidalPS[SlotSequence[1]]]], Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Ce </ci> <apply> <ci> MathieuCharacteristicA </ci> <ci> r </ci> <ci> q </ci> </apply> <ci> q </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <sin /> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> SpheroidalPS </ci> <apply> <plus /> <ci> r </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> q </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <cos /> <ci> z </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["MathieuC", "[", RowBox[List[RowBox[List["MathieuCharacteristicA", "[", RowBox[List["r_", ",", "q_"]], "]"]], ",", "q_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SqrtBox["\[Pi]"], " ", SqrtBox[RowBox[List["Sin", "[", "z", "]"]]], " ", RowBox[List["SpheroidalPS", "[", RowBox[List[RowBox[List["r", "-", FractionBox["1", "2"]]], ",", FractionBox["1", "2"], ",", RowBox[List["2", " ", SqrtBox["q"]]], ",", RowBox[List["Cos", "[", "z", "]"]]]], "]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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