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http://functions.wolfram.com/04.20.07.0002.01
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KroneckerDelta[n, m] == (1/(2 Pi I)) ContourIntegrate[z^(n - m - 1),
{z, Abs[z] == 1}]
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Cell[BoxData[RowBox[List[RowBox[List["KroneckerDelta", "[", RowBox[List["n", ",", "m"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["2", "\[Pi]", " ", "\[ImaginaryI]"]]], RowBox[List["ContourIntegrate", "[", RowBox[List[SuperscriptBox["z", RowBox[List["n", "-", "m", "-", "1"]]], ",", RowBox[List["{", RowBox[List["z", ",", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Equal]", "1"]]]], "}"]]]], "]"]]]]]]]]
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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> <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> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <msub> <mo> ∫ </mo> <mrow> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mi> z </mi> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> <mo> ⩵ </mo> <mn> 1 </mn> </mrow> </msub> <mrow> <msup> <mi> z </mi> <mrow> <mi> n </mi> <mo> - </mo> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> FormBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <apply> <ci> InterpretationBox </ci> <ms> δ </ms> <ci> KroneckerDelta </ci> <apply> <ci> Rule </ci> <ci> Editable </ci> <false /> </apply> <apply> <ci> Rule </ci> <ci> Selectable </ci> <false /> </apply> </apply> <apply> <ci> RowBox </ci> <list> <ms> n </ms> <ms> , </ms> <ms> m </ms> </list> </apply> </apply> <ms> ⩵ </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> FractionBox </ci> <ms> 1 </ms> <apply> <ci> RowBox </ci> <list> <ms> 2 </ms> <ms> π </ms> <ms> ⅈ </ms> </list> </apply> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <apply> <ci> ErrorBox </ci> <ms> ∫ </ms> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms>  </ms> <ms> z </ms> <ms>  </ms> </list> </apply> <ms> ⩵ </ms> <ms> 1 </ms> </list> </apply> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> SuperscriptBox </ci> <ms> z </ms> <apply> <ci> RowBox </ci> <list> <ms> n </ms> <ms> - </ms> <ms> m </ms> <ms> - </ms> <ms> 1 </ms> </list> </apply> </apply> <apply> <ci> RowBox </ci> <list> <ms> ⅆ </ms> <ms> z </ms> </list> </apply> </list> </apply> </list> </apply> </list> </apply> </list> </apply> <ci> TraditionalForm </ci> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KroneckerDelta", "[", RowBox[List["n_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["ContourIntegrate", "[", RowBox[List[SuperscriptBox["z", RowBox[List["n", "-", "m", "-", "1"]]], ",", RowBox[List["{", RowBox[List["z", ",", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Equal]", "1"]]]], "}"]]]], "]"]], RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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