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http://functions.wolfram.com/11.01.21.0001.01
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Integrate[MathieuC[MathieuCharacteristicA[n, q], q, t]
MathieuC[MathieuCharacteristicA[m, q], q, t], {t, -Pi, Pi}] ==
Pi KroneckerDelta[n, m] /; Element[n, Integers] && Element[m, Integers] &&
Element[q, Reals]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", RowBox[List["-", "\[Pi]"]], "\[Pi]"], RowBox[List[RowBox[List["MathieuC", "[", RowBox[List[RowBox[List["MathieuCharacteristicA", "[", RowBox[List["n", ",", "q"]], "]"]], ",", "q", ",", "t"]], "]"]], RowBox[List["MathieuC", "[", RowBox[List[RowBox[List["MathieuCharacteristicA", "[", RowBox[List["m", ",", "q"]], "]"]], ",", "q", ",", "t"]], "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]], "\[Equal]", RowBox[List["\[Pi]", " ", RowBox[List["KroneckerDelta", "[", RowBox[List["n", ",", "m"]], "]"]]]]]], "/;", " ", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["q", "\[Element]", "Reals"]]]]]]]]
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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> <mrow> <msubsup> <mo> ∫ </mo> <mrow> <mo> - </mo> <mi> π </mi> </mrow> <mi> π </mi> </msubsup> <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> n </mi> </msub> <mo> ( </mo> <mi> q </mi> <mo> ) </mo> </mrow> <mo> , </mo> <mi> q </mi> <mo> , </mo> <mi> t </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <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> m </mi> </msub> <mo> ( </mo> <mi> q </mi> <mo> ) </mo> </mrow> <mo> , </mo> <mi> q </mi> <mo> , </mo> <mi> t </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> t </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <msub> <semantics> <mi> δ </mi> <annotation-xml encoding='MathML-Content'> <ci> KroneckerDelta </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> , </mo> <mi> m </mi> </mrow> </msub> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> n </mi> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mi> m </mi> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mi> q </mi> <mo> ∈ </mo> <semantics> <mi> ℝ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalR]", Function[Reals]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <int /> <bvar> <ci> t </ci> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> -1 </cn> <pi /> </apply> </lowlimit> <uplimit> <pi /> </uplimit> <apply> <times /> <apply> <ci> Ce </ci> <apply> <ci> MathieuCharacteristicA </ci> <ci> n </ci> <ci> q </ci> </apply> <ci> q </ci> <ci> t </ci> </apply> <apply> <ci> Ce </ci> <apply> <ci> MathieuCharacteristicA </ci> <ci> m </ci> <ci> q </ci> </apply> <ci> q </ci> <ci> t </ci> </apply> </apply> </apply> <apply> <times /> <pi /> <apply> <ci> KroneckerDelta </ci> <ci> n </ci> <ci> m </ci> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> n </ci> <integers /> </apply> <apply> <in /> <ci> m </ci> <integers /> </apply> <apply> <in /> <ci> q </ci> <reals /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubsuperscriptBox["\[Integral]", RowBox[List["-", "\[Pi]"]], "\[Pi]"], RowBox[List[RowBox[List[RowBox[List["MathieuC", "[", RowBox[List[RowBox[List["MathieuCharacteristicA", "[", RowBox[List["n_", ",", "q_"]], "]"]], ",", "q_", ",", "t_"]], "]"]], " ", RowBox[List["MathieuC", "[", RowBox[List[RowBox[List["MathieuCharacteristicA", "[", RowBox[List["m_", ",", "q_"]], "]"]], ",", "q_", ",", "t_"]], "]"]]]], RowBox[List["\[DifferentialD]", "t_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[Pi]", " ", RowBox[List["KroneckerDelta", "[", RowBox[List["n", ",", "m"]], "]"]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["m", "\[Element]", "Integers"]], "&&", RowBox[List["q", "\[Element]", "Reals"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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