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http://functions.wolfram.com/07.32.03.0145.01
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HypergeometricPFQRegularized[{1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1},
{3/2, 3/2, 3/2, 3/2, 3/2, 3/2}, 1] == Pi^3/15
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Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", FractionBox["1", "2"], ",", FractionBox["1", "2"], ",", FractionBox["1", "2"], ",", FractionBox["1", "2"], ",", FractionBox["1", "2"], ",", "1"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", FractionBox["3", "2"], ",", FractionBox["3", "2"], ",", FractionBox["3", "2"], ",", FractionBox["3", "2"], ",", FractionBox["3", "2"]]], "}"]], ",", "1"]], "]"]], "\[Equal]", FractionBox[SuperscriptBox["\[Pi]", "3"], "15"]]]]]
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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> <mrow> <msub> <mo>   </mo> <mn> 7 </mn> </msub> <msub> <mover> <mi> F </mi> <mo> ~ </mo> </mover> <mn> 6 </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> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["7", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["6", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["1", "2"], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[FractionBox["1", "2"], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[FractionBox["1", "2"], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[FractionBox["1", "2"], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[FractionBox["1", "2"], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[FractionBox["1", "2"], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox["1", HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["3", "2"], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[FractionBox["3", "2"], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[FractionBox["3", "2"], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[FractionBox["3", "2"], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[FractionBox["3", "2"], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[FractionBox["3", "2"], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox["1", HypergeometricPFQRegularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQRegularized] </annotation> </semantics> <mo> ⩵ </mo> <mfrac> <msup> <mi> π </mi> <mn> 3 </mn> </msup> <mn> 15 </mn> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQRegularized </ci> <list> <cn type='rational'> 1 <sep /> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> <cn type='integer'> 1 </cn> </list> <list> <cn type='rational'> 3 <sep /> 2 </cn> <cn type='rational'> 3 <sep /> 2 </cn> <cn type='rational'> 3 <sep /> 2 </cn> <cn type='rational'> 3 <sep /> 2 </cn> <cn type='rational'> 3 <sep /> 2 </cn> <cn type='rational'> 3 <sep /> 2 </cn> </list> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 15 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", FractionBox["1", "2"], ",", FractionBox["1", "2"], ",", FractionBox["1", "2"], ",", FractionBox["1", "2"], ",", FractionBox["1", "2"], ",", "1"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", FractionBox["3", "2"], ",", FractionBox["3", "2"], ",", FractionBox["3", "2"], ",", FractionBox["3", "2"], ",", FractionBox["3", "2"]]], "}"]], ",", "1"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[SuperscriptBox["\[Pi]", "3"], "15"]]]]] |
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Date Added to functions.wolfram.com (modification date)
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