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http://functions.wolfram.com/07.23.26.0033.01
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Hypergeometric2F1[a, b, 2 b, -((4 Sqrt[z])/(-1 + Sqrt[z])^2)]/
((1 + Sqrt[z])^(2 a) ((-1 + Sqrt[z])^2/(1 + Sqrt[z])^2)^a) ==
(1/Gamma[a]) Gamma[1/2 + b] Gamma[1/2 - a + b]
MeijerG[{{1 - a}, {1/2 - a + b}}, {{0}, {1/2 - b}}, z]
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z_"]]], ")"]], RowBox[List[RowBox[List["-", "2"]], " ", "a_"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z_"]]], ")"]], "2"], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z_"]]], ")"]], "2"]], ")"]], RowBox[List["-", "a_"]]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List["a_", ",", "b_", ",", RowBox[List["2", " ", "b_"]], ",", RowBox[List["-", FractionBox[RowBox[List["4", " ", SqrtBox["z_"]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z_"]]], ")"]], "2"]]]]]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", "b"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "-", "a", "+", "b"]], "]"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", "-", "a"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], "-", "a", "+", "b"]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], "-", "b"]], "}"]]]], "}"]], ",", "z"]], "]"]]]], RowBox[List["Gamma", "[", "a", "]"]]]]]]] |
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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,b2},z] | HypergeometricPFQ[{a1,a2},{b1,b2,b3},z] | HypergeometricPFQ[{a1,a2,a3},{b1,b2},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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