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variants of this functions
PolyGamma




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > PolyGamma[nu,z] > Transformations > Products, sums, and powers of the direct function > Sums of the direct function





http://functions.wolfram.com/06.15.16.0012.01









  


  








Input Form





PolyGamma[0, z] + PolyGamma[0, z + 1/2] == 2 PolyGamma[0, 2 z] - 2 Log[2]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["PolyGamma", "[", RowBox[List["0", ",", "z"]], "]"]], "+", RowBox[List["PolyGamma", "[", RowBox[List["0", ",", RowBox[List["z", "+", FractionBox["1", "2"]]]]], "]"]]]], "\[Equal]", RowBox[List[RowBox[List["2", RowBox[List["PolyGamma", "[", RowBox[List["0", ",", RowBox[List["2", " ", "z"]]]], "]"]]]], "-", RowBox[List["2", RowBox[List["Log", "[", "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> <mrow> <msup> <semantics> <mi> &#968; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Psi]&quot;, PolyGamma] </annotation> </semantics> <mrow> <mo> ( </mo> <mn> 0 </mn> <mo> ) </mo> </mrow> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <msup> <semantics> <mi> &#968; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Psi]&quot;, PolyGamma] </annotation> </semantics> <mrow> <mo> ( </mo> <mn> 0 </mn> <mo> ) </mo> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <msup> <semantics> <mi> &#968; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Psi]&quot;, PolyGamma] </annotation> </semantics> <mrow> <mo> ( </mo> <mn> 0 </mn> <mo> ) </mo> </mrow> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <ci> PolyGamma </ci> <cn type='integer'> 0 </cn> <apply> <plus /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <ci> PolyGamma </ci> <cn type='integer'> 0 </cn> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> PolyGamma </ci> <cn type='integer'> 0 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ln /> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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


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





2001-10-29