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 | | http://functions.wolfram.com/07.32.03.0147.01 | 
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 | | HypergeometricPFQRegularized[{1, 1, 1, d, d, 2 - d, 2 - d}, 
   {2, 2, 1 + d, 1 + d, 3 - d, 3 - d}, -1] == 
  (Sin[d Pi]^2/(12 (-1 + d)^8 Pi^2)) (Pi^2 (1 - d)^2 + 12 - 
    9 Pi (1 - d) Csc[Pi d] + 3 Pi^2 (1 - d)^2 Cos[Pi d] Csc[Pi d]^2) /; d != 1 | 
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 | | Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", "1", ",", "1", ",", "d", ",", "d", ",", RowBox[List["2", "-", "d"]], ",", RowBox[List["2", "-", "d"]]]], "}"]], ",", RowBox[List["{", RowBox[List["2", ",", "2", ",", RowBox[List["1", "+", "d"]], ",", RowBox[List["1", "+", "d"]], ",", RowBox[List["3", "-", "d"]], ",", RowBox[List["3", "-", "d"]]]], "}"]], ",", RowBox[List["-", "1"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox[SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["d", " ", "\[Pi]"]], "]"]], "2"], RowBox[List["12", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "d"]], ")"]], "8"], " ", SuperscriptBox["\[Pi]", "2"]]]], " ", RowBox[List["(", " ", RowBox[List[RowBox[List[SuperscriptBox["\[Pi]", "2"], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "d"]], ")"]], "2"]]], "+", "12", "-", RowBox[List["9", "\[Pi]", RowBox[List["(", RowBox[List["1", "-", "d"]], ")"]], RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", "d"]], "]"]]]], "+", RowBox[List["3", SuperscriptBox["\[Pi]", "2"], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "d"]], ")"]], "2"], RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", "d"]], "]"]], SuperscriptBox[RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", "d"]], "]"]], "2"]]]]], ")"]]]]]], "/;", RowBox[List["d", "\[NotEqual]", "1"]]]]]] | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", "1", ",", "1", ",", "d_", ",", "d_", ",", RowBox[List["2", "-", "d_"]], ",", RowBox[List["2", "-", "d_"]]]], "}"]], ",", RowBox[List["{", RowBox[List["2", ",", "2", ",", RowBox[List["1", "+", "d_"]], ",", RowBox[List["1", "+", "d_"]], ",", RowBox[List["3", "-", "d_"]], ",", RowBox[List["3", "-", "d_"]]]], "}"]], ",", RowBox[List["-", "1"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["d", " ", "\[Pi]"]], "]"]], "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "d"]], ")"]], "2"]]], "+", "12", "-", RowBox[List["9", " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["1", "-", "d"]], ")"]], " ", RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", "d"]], "]"]]]], "+", RowBox[List["3", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "d"]], ")"]], "2"], " ", RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", "d"]], "]"]], " ", SuperscriptBox[RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", "d"]], "]"]], "2"]]]]], ")"]]]], RowBox[List["12", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "d"]], ")"]], "8"], " ", SuperscriptBox["\[Pi]", "2"]]]], "/;", RowBox[List["d", "\[NotEqual]", "1"]]]]]]]] | 
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 | | Date Added to functions.wolfram.com (modification date) | 
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