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LogIntegral




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > LogIntegral[z] > Representations through more general functions > Through other functions





http://functions.wolfram.com/06.36.26.0004.01









  


  








Input Form





LogIntegral[z] == -Gamma[0, -Log[z]] + (1/2) (Log[Log[z]] - Log[1/Log[z]]) - Log[-Log[z]]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["LogIntegral", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List["-", RowBox[List["Gamma", "[", RowBox[List["0", ",", RowBox[List["-", RowBox[List["Log", "[", "z", "]"]]]]]], "]"]]]], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["Log", "[", "z", "]"]], "]"]], "-", RowBox[List["Log", "[", FractionBox["1", RowBox[List["Log", "[", "z", "]"]]], "]"]]]], ")"]]]], "-", RowBox[List["Log", "[", RowBox[List["-", RowBox[List["Log", "[", "z", "]"]]]], "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> li </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> LogIntegral </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Gamma </ci> <cn type='integer'> 0 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <ln /> <apply> <ln /> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <ln /> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LogIntegral", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", RowBox[List["Gamma", "[", RowBox[List["0", ",", RowBox[List["-", RowBox[List["Log", "[", "z", "]"]]]]]], "]"]]]], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["Log", "[", "z", "]"]], "]"]], "-", RowBox[List["Log", "[", FractionBox["1", RowBox[List["Log", "[", "z", "]"]]], "]"]]]], ")"]]]], "-", RowBox[List["Log", "[", RowBox[List["-", RowBox[List["Log", "[", "z", "]"]]]], "]"]]]]]]]]


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





2001-10-29