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MathieuCharacteristicA




Mathematica Notation

Traditional Notation









Mathieu and Spheroidal Functions > MathieuCharacteristicA[r,q] > Representations through more general functions > Through other functions





http://functions.wolfram.com/11.05.26.0001.01









  


  








Input Form





MathieuCharacteristicA[r, q] == SpheroidalEigenvalue[r - 1/2, 1/2, 2 Sqrt[q]] + 1/4 + 2 q








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["MathieuCharacteristicA", "[", RowBox[List["r", ",", "q"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["SpheroidalEigenvalue", "[", RowBox[List[RowBox[List["r", "-", RowBox[List["1", "/", "2"]]]], ",", RowBox[List["1", "/", "2"]], ",", RowBox[List["2", SqrtBox["q"]]]]], "]"]], "+", FractionBox["1", "4"], "+", RowBox[List["2", "q"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <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> &#63449; </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> q </mi> </mrow> <mo> + </mo> <semantics> <mrow> <msub> <mi> &#955; </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> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mi> q </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubscriptBox[&quot;\[Lambda]&quot;, RowBox[List[TagBox[RowBox[List[&quot;r&quot;, &quot;-&quot;, FractionBox[&quot;1&quot;, &quot;2&quot;]]], SpheroidalEigenvalue, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;1&quot;, &quot;2&quot;], SpheroidalEigenvalue, Rule[Editable, True], Rule[Selectable, True]]]]], &quot;(&quot;, TagBox[RowBox[List[&quot;2&quot;, &quot; &quot;, SqrtBox[&quot;q&quot;]]], SpheroidalEigenvalue, Rule[Editable, True], Rule[Selectable, True]], &quot;)&quot;]], InterpretTemplate[Function[SpheroidalEigenvalue[SlotSequence[1]]]], Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> MathieuCharacteristicA </ci> <ci> r </ci> <ci> q </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> q </ci> </apply> <apply> <ci> SpheroidalEigenvalue </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> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["MathieuCharacteristicA", "[", RowBox[List["r_", ",", "q_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["SpheroidalEigenvalue", "[", RowBox[List[RowBox[List["r", "-", FractionBox["1", "2"]]], ",", FractionBox["1", "2"], ",", RowBox[List["2", " ", SqrtBox["q"]]]]], "]"]], "+", FractionBox["1", "4"], "+", RowBox[List["2", " ", "q"]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2007-05-02