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http://functions.wolfram.com/06.15.03.0045.01
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PolyGamma[2, 5/6] == 4 Sqrt[3] Pi^3 - 182 Zeta[3]
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Cell[BoxData[RowBox[List[RowBox[List["PolyGamma", "[", RowBox[List["2", ",", FractionBox["5", "6"]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["4", " ", SqrtBox["3"], " ", SuperscriptBox["\[Pi]", "3"]]], "-", RowBox[List["182", " ", RowBox[List["Zeta", "[", "3", "]"]]]]]]]]]]
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<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> ψ </mi> <annotation encoding='Mathematica'> TagBox["\[Psi]", PolyGamma] </annotation> </semantics> <mrow> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </msup> <mo> ( </mo> <mfrac> <mn> 5 </mn> <mn> 6 </mn> </mfrac> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msqrt> <mn> 3 </mn> </msqrt> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 182 </mn> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> PolyGamma </ci> <cn type='integer'> 2 </cn> <cn type='rational'> 5 <sep /> 6 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <pi /> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 182 </cn> <apply> <ci> Zeta </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["PolyGamma", "[", RowBox[List["2", ",", FractionBox["5", "6"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["4", " ", SqrtBox["3"], " ", SuperscriptBox["\[Pi]", "3"]]], "-", RowBox[List["182", " ", RowBox[List["Zeta", "[", "3", "]"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
