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http://functions.wolfram.com/10.01.03.0057.01
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Zeta[3] == (29/24) HypergeometricPFQ[{1/2, 1/2, 1, 1, 1, 1,
(1/28) (48 - I Sqrt[6]), (1/28) (48 + I Sqrt[6])},
{4/3, 5/3, 3/2, 3/2, 2, (1/28) (20 - I Sqrt[6]), (1/28) (20 + I Sqrt[6])},
-(1/27)]
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Cell[BoxData[RowBox[List[RowBox[List["Zeta", "[", "3", "]"]], "\[Equal]", RowBox[List[FractionBox["29", "24"], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", FractionBox["1", "2"], ",", "1", ",", "1", ",", "1", ",", "1", ",", RowBox[List[FractionBox["1", "28"], " ", RowBox[List["(", RowBox[List["48", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["6"]]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "28"], " ", RowBox[List["(", RowBox[List["48", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["6"]]]]], ")"]]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["4", "3"], ",", FractionBox["5", "3"], ",", FractionBox["3", "2"], ",", FractionBox["3", "2"], ",", "2", ",", RowBox[List[FractionBox["1", "28"], " ", RowBox[List["(", RowBox[List["20", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["6"]]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "28"], " ", RowBox[List["(", RowBox[List["20", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["6"]]]]], ")"]]]]]], "}"]], ",", RowBox[List["-", FractionBox["1", "27"]]]]], "]"]]]]]]]]
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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> <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> <mo>  </mo> <mrow> <mfrac> <mn> 29 </mn> <mn> 24 </mn> </mfrac> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 8 </mn> </msub> <msub> <mi> F </mi> <mn> 7 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mn> 1 </mn> <mo> , </mo> <mn> 1 </mn> <mo> , </mo> <mn> 1 </mn> <mo> , </mo> <mn> 1 </mn> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 28 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 48 </mn> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msqrt> <mn> 6 </mn> </msqrt> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 28 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 48 </mn> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msqrt> <mn> 6 </mn> </msqrt> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 4 </mn> <mn> 3 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 5 </mn> <mn> 3 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mn> 2 </mn> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 28 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 20 </mn> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msqrt> <mn> 6 </mn> </msqrt> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 28 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 20 </mn> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msqrt> <mn> 6 </mn> </msqrt> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 27 </mn> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "8"], SubscriptBox["F", "7"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["1", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["1", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["1", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["1", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["1", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["1", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "28"], " ", RowBox[List["(", RowBox[List["48", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["6"]]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "28"], " ", RowBox[List["(", RowBox[List["48", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["6"]]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["4", "3"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["5", "3"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["2", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "28"], " ", RowBox[List["(", RowBox[List["20", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["6"]]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "28"], " ", RowBox[List["(", RowBox[List["20", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["6"]]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List["-", FractionBox["1", "27"]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Zeta </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='rational'> 29 <sep /> 24 </cn> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='rational'> 1 <sep /> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> <cn type='integer'> 1 </cn> <cn type='integer'> 1 </cn> <cn type='integer'> 1 </cn> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 28 </cn> <apply> <plus /> <cn type='integer'> 48 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 6 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 28 </cn> <apply> <plus /> <cn type='integer'> 48 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 6 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </list> <list> <cn type='rational'> 4 <sep /> 3 </cn> <cn type='rational'> 5 <sep /> 3 </cn> <cn type='rational'> 3 <sep /> 2 </cn> <cn type='rational'> 3 <sep /> 2 </cn> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 28 </cn> <apply> <plus /> <cn type='integer'> 20 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 6 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 28 </cn> <apply> <plus /> <cn type='integer'> 20 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 6 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 27 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Zeta", "[", "3", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["29", "24"], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", FractionBox["1", "2"], ",", "1", ",", "1", ",", "1", ",", "1", ",", RowBox[List[FractionBox["1", "28"], " ", RowBox[List["(", RowBox[List["48", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["6"]]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "28"], " ", RowBox[List["(", RowBox[List["48", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["6"]]]]], ")"]]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["4", "3"], ",", FractionBox["5", "3"], ",", FractionBox["3", "2"], ",", FractionBox["3", "2"], ",", "2", ",", RowBox[List[FractionBox["1", "28"], " ", RowBox[List["(", RowBox[List["20", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["6"]]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "28"], " ", RowBox[List["(", RowBox[List["20", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["6"]]]]], ")"]]]]]], "}"]], ",", RowBox[List["-", FractionBox["1", "27"]]]]], "]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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