PolyGamma[-(3/2)] == 8/3 - EulerGamma - Log[4]

Cell[BoxData[RowBox[List[RowBox[List["PolyGamma", "[", RowBox[List["-", FractionBox["3", "2"]]], "]"]], "\[Equal]", RowBox[List[FractionBox["8", "3"], "-", "EulerGamma", "-", RowBox[List["Log", "[", "4", "]"]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <mi> &#968; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Psi]&quot;, PolyGamma] </annotation> </semantics> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 8 </mn> <mn> 3 </mn> </mfrac> <mo> - </mo> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[EulerGamma]] </annotation> </semantics> <mo> - </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 4 </mn> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> PolyGamma </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <plus /> <cn type='rational'> 8 <sep /> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <eulergamma /> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["PolyGamma", "[", RowBox[List["-", FractionBox["3", "2"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["8", "3"], "-", "EulerGamma", "-", RowBox[List["Log", "[", "4", "]"]]]]]]]]

2001-10-29