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Power




Mathematica Notation

Traditional Notation









Elementary Functions > Power[z,a] > Series representations > Residue representations > Representations of za





http://functions.wolfram.com/01.02.06.0080.01









  


  








Input Form





z^a == Sum[Residue[Gamma[s]/((-a) Log[z])^s, {s, -j}], {j, 0, Infinity}]








Standard Form





Cell[BoxData[RowBox[List[SuperscriptBox["z", "a"], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "\[Infinity]"], RowBox[List["Residue", "[", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], " ", RowBox[List["Log", "[", "z", "]"]]]], ")"]], RowBox[List["-", "s"]]], RowBox[List["Gamma", "[", "s", "]"]]]], ",", RowBox[List["{", RowBox[List["s", ",", RowBox[List["-", "j"]]]], "}"]]]], "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <msup> <mi> z </mi> <mi> a </mi> </msup> <mo> &#10869; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> &#8734; </mi> </munderover> <mrow> <mi> res </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> s </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mo> { </mo> <mrow> <mi> s </mi> <mo> , </mo> <mrow> <mo> - </mo> <mi> j </mi> </mrow> </mrow> <mo> } </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <power /> <ci> z </ci> <ci> a </ci> </apply> <apply> <sum /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <ci> Residue </ci> <apply> <times /> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <ln /> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> <apply> <ci> Gamma </ci> <ci> s </ci> </apply> </apply> <list> <ci> s </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> </list> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox["z_", "a_"], "]"]], "\[RuleDelayed]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "\[Infinity]"], RowBox[List["Residue", "[", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], " ", RowBox[List["Log", "[", "z", "]"]]]], ")"]], RowBox[List["-", "s"]]], " ", RowBox[List["Gamma", "[", "s", "]"]]]], ",", RowBox[List["{", RowBox[List["s", ",", RowBox[List["-", "j"]]]], "}"]]]], "]"]]]]]]]]


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





2007-05-02