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Abs






Mathematica Notation

Traditional Notation









Complex Components > Abs[z] > Integration > Contour integration





http://functions.wolfram.com/12.01.21.0008.01









  


  










Input Form





ContourIntegrate[z^(m - 1)/Abs[z - k]^(2 (n + 1)), {z, ρ Exp[I φ], {0, 2 Pi}}] == 2*Pi*I*(UnitStep[ρ - Abs[w]]*Sum[Binomial[n + k, k]* Binomial[n + m, n - k]*((w^m*Abs[w]^(2*k))/ (ρ^2 - Abs[w]^2)^(n + k + 1)), {k, 0, n}] + UnitStep[Abs[w] - ρ]*Sum[Binomial[n + k, k]* Binomial[n + m, n - k]*(ρ^(2*(m + k))/ (Conjugate[w]^m*(Abs[w]^2 - ρ^2)^(n + k + 1))), {k, 0, n}]) /; n ∈ Integers && n >= 0 && m ∈ Integers && m >= 0 && w != 0 && Abs[w] != ρ










Standard Form





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MathML Form







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</ms> <ms> w </ms> <ms> &#62980; </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> 2 </ms> <ms> k </ms> </list> </apply> </apply> </list> </apply> <apply> <ci> SuperscriptBox </ci> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SuperscriptBox </ci> <ms> &#961; </ms> <ms> 2 </ms> </apply> <ms> - </ms> <apply> <ci> SuperscriptBox </ci> <apply> <ci> RowBox </ci> <list> <ms> &#62979; </ms> <ms> w </ms> <ms> &#62980; </ms> </list> </apply> <ms> 2 </ms> </apply> </list> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> k </ms> <ms> + </ms> <ms> n </ms> <ms> + </ms> <ms> 1 </ms> </list> </apply> </apply> </apply> </list> </apply> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> </list> </apply> <ms> /; </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> n </ms> <ms> &#8712; </ms> <ms> &#8469; </ms> </list> </apply> <ms> &#8743; </ms> <apply> <ci> RowBox </ci> <list> <ms> m </ms> <ms> &#8712; </ms> <ms> &#8469; </ms> </list> </apply> <ms> &#8743; </ms> <apply> <ci> RowBox </ci> <list> <ms> w </ms> <ms> &#8800; </ms> <ms> 0 </ms> </list> </apply> <ms> &#8743; </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> &#62979; </ms> <ms> w </ms> <ms> &#62980; </ms> </list> </apply> <ms> &#8800; </ms> <ms> &#961; </ms> </list> </apply> </list> </apply> </list> </apply> <ci> TraditionalForm </ci> </apply> </annotation-xml> </semantics> </math>










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





2002-12-18





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