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LogGamma




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/06.11.27.0001.01









  


  








Input Form





LogGamma[z] == Log[Gamma[z]] /; Inequality[0, Less, Re[z], LessEqual, 2] && Abs[Im[z]] <= 7/2








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["LogGamma", "[", "z", "]"]], "\[Equal]", RowBox[List["Log", "[", RowBox[List["Gamma", "[", "z", "]"]], "]"]]]], "/;", RowBox[List[RowBox[List["0", "<", RowBox[List["Re", "[", "z", "]"]], "\[LessEqual]", "2"]], "\[And]", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Im", "[", "z", "]"]], "]"]], "\[LessEqual]", FractionBox["7", "2"]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mstyle scriptlevel='0'> <mrow> <mi> log&#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mstyle> <mo> &#10869; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mn> 0 </mn> <mo> &lt; </mo> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8804; </mo> <mn> 2 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> &#8804; </mo> <mfrac> <mn> 7 </mn> <mn> 2 </mn> </mfrac> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <times /> <ci> log&#915; </ci> <ci> z </ci> </apply> <apply> <ln /> <apply> <ci> Gamma </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <and /> <apply> <ci> Inequality </ci> <cn type='integer'> 0 </cn> <lt /> <apply> <real /> <ci> z </ci> </apply> <leq /> <cn type='integer'> 2 </cn> </apply> <apply> <leq /> <apply> <abs /> <apply> <imaginary /> <ci> z </ci> </apply> </apply> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LogGamma", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Log", "[", RowBox[List["Gamma", "[", "z", "]"]], "]"]], "/;", RowBox[List[RowBox[List["0", "<", RowBox[List["Re", "[", "z", "]"]], "\[LessEqual]", "2"]], "&&", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Im", "[", "z", "]"]], "]"]], "\[LessEqual]", FractionBox["7", "2"]]]]]]]]]]]


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





2001-10-29