Limit[(1/Sqrt[a]) MathieuCPrime[a, q, z/Sqrt[a]], a -> Infinity] == -Sin[z] /; Element[q, Reals]

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Limit", "[", RowBox[List[RowBox[List[FractionBox["1", SqrtBox["a"]], RowBox[List["MathieuCPrime", "[", RowBox[List["a", ",", "q", ",", FractionBox["z", SqrtBox["a"]]]], "]"]]]], ",", RowBox[List["a", "\[Rule]", "\[Infinity]"]]]], "]"]], "\[Equal]", RowBox[List["-", RowBox[List["Sin", "[", "z", "]"]]]]]], "/;", RowBox[List["Element", "[", RowBox[List["q", ",", "Reals"]], "]"]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <munder> <mi> lim </mi> <mrow> <mi> a </mi> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mi> &#8734; </mi> </mrow> </munder> <mo> &#8290; </mo> <mtext> &#8201; </mtext> <mrow> <mfrac> <mn> 1 </mn> <msqrt> <mi> a </mi> </msqrt> </mfrac> <mo> &#8290; </mo> <mrow> <msup> <mi> Ce </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> q </mi> <mo> , </mo> <mfrac> <mi> z </mi> <msqrt> <mi> a </mi> </msqrt> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mo> - </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> q </mi> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <limit /> <bvar> <ci> a </ci> </bvar> <condition> <apply> <tendsto /> <ci> a </ci> <infinity /> </apply> </condition> <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> <apply> <partialdiff /> <list> <cn type='integer'> 1 </cn> </list> <ci> Ce </ci> </apply> <ci> a </ci> <ci> q </ci> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <sin /> <ci> z </ci> </apply> </apply> </apply> <apply> <in /> <ci> q </ci> <reals /> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Limit", "[", RowBox[List[FractionBox[RowBox[List["MathieuCPrime", "[", RowBox[List["a_", ",", "q_", ",", FractionBox["z_", SqrtBox["a_"]]]], "]"]], SqrtBox["a_"]], ",", RowBox[List["a_", "\[Rule]", "\[Infinity]"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", RowBox[List["Sin", "[", "z", "]"]]]], "/;", RowBox[List["q", "\[Element]", "Reals"]]]]]]]]

2001-10-29