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CoshIntegral




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > CoshIntegral[z] > Representations through equivalent functions > With related functions





http://functions.wolfram.com/06.40.27.0002.01









  


  








Input Form





CoshIntegral[z] == (1/4) (2 (ExpIntegralEi[-z] + ExpIntegralEi[z]) + Log[-(1/z)] + Log[1/z] - Log[-z] + 3 Log[z])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["CoshIntegral", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["ExpIntegralEi", "[", RowBox[List["-", "z"]], "]"]], "+", RowBox[List["ExpIntegralEi", "[", "z", "]"]]]], ")"]]]], "+", RowBox[List["Log", "[", RowBox[List["-", FractionBox["1", "z"]]], "]"]], "+", RowBox[List["Log", "[", FractionBox["1", "z"], "]"]], "-", RowBox[List["Log", "[", RowBox[List["-", "z"]], "]"]], "+", RowBox[List["3", " ", 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> Chi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Ei </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> Ei </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> CoshIntegral </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <ci> ExpIntegralEi </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <ln /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ln /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <ln /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["CoshIntegral", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["ExpIntegralEi", "[", RowBox[List["-", "z"]], "]"]], "+", RowBox[List["ExpIntegralEi", "[", "z", "]"]]]], ")"]]]], "+", RowBox[List["Log", "[", RowBox[List["-", FractionBox["1", "z"]]], "]"]], "+", RowBox[List["Log", "[", FractionBox["1", "z"], "]"]], "-", RowBox[List["Log", "[", RowBox[List["-", "z"]], "]"]], "+", RowBox[List["3", " ", RowBox[List["Log", "[", "z", "]"]]]]]], ")"]]]]]]]]


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





2001-10-29