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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.am0u.01

 Input Form

 Hypergeometric2F1[3, 3, 7/4, z] == (1/8192) (3 ((72 (37 + 28 z))/(-1 + z)^4 - (10 Sqrt[2] (5 + 80 z + 32 z^2) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/((1 - z)^(17/4) z^(3/4)) - (10 Sqrt[2] (5 + 80 z + 32 z^2) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/((1 - z)^(17/4) z^(3/4)) + (5 Sqrt[2] (5 + 80 z + 32 z^2) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/((1 - z)^(17/4) z^(3/4)) - (5 Sqrt[2] (5 + 80 z + 32 z^2) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/((1 - z)^(17/4) z^(3/4))))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["3", ",", "3", ",", FractionBox["7", "4"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "8192"], RowBox[List["(", RowBox[List["3", " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["72", " ", RowBox[List["(", RowBox[List["37", "+", RowBox[List["28", " ", "z"]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "4"]], "-", FractionBox[RowBox[List["10", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["80", " ", "z"]], "+", RowBox[List["32", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "-", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]]]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["17", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]]]]], "-", FractionBox[RowBox[List["10", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["80", " ", "z"]], "+", RowBox[List["32", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "+", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]]]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["17", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]]]]], "+", FractionBox[RowBox[List["5", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["80", " ", "z"]], "+", RowBox[List["32", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", FractionBox[RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]], "+", FractionBox[SqrtBox["z"], SqrtBox[RowBox[List["1", "-", "z"]]]]]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["17", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]]]]], "-", FractionBox[RowBox[List["5", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["80", " ", "z"]], "+", RowBox[List["32", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]], "+", FractionBox[SqrtBox["z"], SqrtBox[RowBox[List["1", "-", "z"]]]]]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["17", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( 3 , 3 ; 7 4 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["3", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["3", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["7", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] 1 8192 ( 3 ( 72 ( 28 z + 37 ) ( z - 1 ) 4 - 10 2 ( 32 z 2 + 80 z + 5 ) tan - 1 ( 1 - z 4 2 1 - z 4 , - z 4 2 1 - z 4 ) ( 1 - z ) 17 / 4 z 3 / 4 - 10 2 ( 32 z 2 + 80 z + 5 ) tan - 1 ( z 4 2 1 - z 4 + 1 , - z 4 2 1 - z 4 ) ( 1 - z ) 17 / 4 z 3 / 4 + 5 2 ( 32 z 2 + 80 z + 5 ) log ( z 1 - z - 2 z 4 1 - z 4 + 1 ) ( 1 - z ) 17 / 4 z 3 / 4 - 5 2 ( 32 z 2 + 80 z + 5 ) log ( z 1 - z + 2 z 4 1 - z 4 + 1 ) ( 1 - z ) 17 / 4 z 3 / 4 ) ) HypergeometricPFQ 3 3 7 4 z 1 8192 3 72 28 z 37 z -1 4 -1 -1 10 2 1 2 32 z 2 80 z 5 1 -1 z 1 4 2 1 2 1 -1 z 1 4 -1 -1 z 1 4 2 1 2 1 -1 z 1 4 -1 1 -1 z 17 4 z 3 4 -1 -1 10 2 1 2 32 z 2 80 z 5 z 1 4 2 1 2 1 -1 z 1 4 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 4 -1 1 -1 z 17 4 z 3 4 -1 5 2 1 2 32 z 2 80 z 5 z 1 2 1 -1 z 1 2 -1 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 1 -1 z 17 4 z 3 4 -1 -1 5 2 1 2 32 z 2 80 z 5 z 1 2 1 -1 z 1 2 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 1 -1 z 17 4 z 3 4 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List["3", ",", "3", ",", FractionBox["7", "4"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["3", " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["72", " ", RowBox[List["(", RowBox[List["37", "+", RowBox[List["28", " ", "z"]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "4"]], "-", FractionBox[RowBox[List["10", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["80", " ", "z"]], "+", RowBox[List["32", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "-", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]]]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["17", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]]]]], "-", FractionBox[RowBox[List["10", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["80", " ", "z"]], "+", RowBox[List["32", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "+", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]]]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["17", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]]]]], "+", FractionBox[RowBox[List["5", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["80", " ", "z"]], "+", RowBox[List["32", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", FractionBox[RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]], "+", FractionBox[SqrtBox["z"], SqrtBox[RowBox[List["1", "-", "z"]]]]]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["17", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]]]]], "-", FractionBox[RowBox[List["5", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["80", " ", "z"]], "+", RowBox[List["32", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]], "+", FractionBox[SqrtBox["z"], SqrtBox[RowBox[List["1", "-", "z"]]]]]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["17", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]]]]]]], ")"]]]], "8192"]]]]]

 Date Added to functions.wolfram.com (modification date)

 2007-05-02