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http://functions.wolfram.com/07.27.26.0009.01
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HypergeometricPFQ[{a, a + 1/2, b}, {c, 2 a + b - c + 1}, (4 z)/(1 + z)^2]/
(1 + z)^(2 a) == ((Gamma[c] Gamma[2 a + b - c + 1])/
(Gamma[2 a] Gamma[2 a - c + 1] Gamma[c - b]))
MeijerG[{{1 - 2 a, c - 2 a, 1 + b - c}, {}}, {{0}, {1 - c, c - b - 2 a}},
z] /; Abs[z] < 1
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List[RowBox[List["-", "2"]], " ", "a"]]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["a", ",", RowBox[List["a", "+", FractionBox["1", "2"]]], ",", "b"]], "}"]], ",", RowBox[List["{", RowBox[List["c", ",", RowBox[List[RowBox[List["2", " ", "a"]], "+", "b", "-", "c", "+", "1"]]]], "}"]], ",", FractionBox[RowBox[List["4", " ", "z"]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "2"]]]], "]"]]]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", "c", "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["2", " ", "a"]], "+", "b", "-", "c", "+", "1"]], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List["2", " ", "a"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["2", " ", "a"]], "-", "c", "+", "1"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["c", "-", "b"]], "]"]]]]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", RowBox[List["2", " ", "a"]]]], ",", RowBox[List["c", "-", RowBox[List["2", " ", "a"]]]], ",", RowBox[List["1", "+", "b", "-", "c"]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", "c"]], ",", RowBox[List["c", "-", "b", "-", RowBox[List["2", " ", "a"]]]]]], "}"]]]], "}"]], ",", "z"]], "]"]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "<", "1"]]]]]]
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z_"]], ")"]], RowBox[List[RowBox[List["-", "2"]], " ", "a_"]]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["a_", ",", RowBox[List["a_", "+", FractionBox["1", "2"]]], ",", "b_"]], "}"]], ",", RowBox[List["{", RowBox[List["c_", ",", RowBox[List[RowBox[List["2", " ", "a_"]], "+", "b_", "-", "c_", "+", "1"]]]], "}"]], ",", FractionBox[RowBox[List["4", " ", "z_"]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z_"]], ")"]], "2"]]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Gamma", "[", "c", "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["2", " ", "a"]], "+", "b", "-", "c", "+", "1"]], "]"]]]], ")"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", RowBox[List["2", " ", "a"]]]], ",", RowBox[List["c", "-", RowBox[List["2", " ", "a"]]]], ",", RowBox[List["1", "+", "b", "-", "c"]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", "c"]], ",", RowBox[List["c", "-", "b", "-", RowBox[List["2", " ", "a"]]]]]], "}"]]]], "}"]], ",", "z"]], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List["2", " ", "a"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["2", " ", "a"]], "-", "c", "+", "1"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["c", "-", "b"]], "]"]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "<", "1"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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HypergeometricPFQ[{},{},z] | HypergeometricPFQ[{},{b},z] | HypergeometricPFQ[{a},{},z] | HypergeometricPFQ[{a},{b},z] | HypergeometricPFQ[{a1},{b1,b2},z] | HypergeometricPFQ[{a1,a2},{b1},z] | HypergeometricPFQ[{a1,a2},{b1,b2},z] | HypergeometricPFQ[{a1,a2},{b1,b2,b3},z] | HypergeometricPFQ[{a1,a2,a3,a4},{b1,b2,b3},z] | HypergeometricPFQ[{a1,a2,a3,a4,a5},{b1,b2,b3,b4},z] | HypergeometricPFQ[{a1,a2,a3,a4,a5,a6},{b1,b2,b3,b4,b5},z] | HypergeometricPFQ[{a1,...,ap},{b1,...,bq},z] | |
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