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variants of this functions
PolyGamma




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > PolyGamma[nu,z] > Specific values > Specialized values > For fixed z





http://functions.wolfram.com/06.15.03.0028.01









  


  








Input Form





PolyGamma[-1, z] == -Log[z] + Log[Gamma[1 + z]]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["PolyGamma", "[", RowBox[List[RowBox[List["-", "1"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", RowBox[List["Log", "[", "z", "]"]]]], "+", RowBox[List["Log", "[", RowBox[List["Gamma", "[", RowBox[List["1", "+", "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> <msup> <semantics> <mi> &#968; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Psi]&quot;, PolyGamma] </annotation> </semantics> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> PolyGamma </ci> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <apply> <plus /> <apply> <ln /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <ci> z </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["PolyGamma", "[", RowBox[List[RowBox[List["-", "1"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", RowBox[List["Log", "[", "z", "]"]]]], "+", RowBox[List["Log", "[", RowBox[List["Gamma", "[", RowBox[List["1", "+", "z"]], "]"]], "]"]]]]]]]]


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





2007-05-02