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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.aje9.01

 Input Form

 Hypergeometric2F1[1, 2, 13/4, z] == (1/(32 z^(9/4))) (9 (-8 (-5 + z) z^(1/4) + 10 Sqrt[2] (1 - z)^(1/4) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] + 10 Sqrt[2] (1 - z)^(1/4) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] + 5 Sqrt[2] (1 - z)^(1/4) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]] - 5 Sqrt[2] (1 - z)^(1/4) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]]))

 Standard Form

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 MathML Form

 2 F 1 ( 1 , 2 ; 13 4 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["1", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["2", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["13", "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 32 z 9 / 4 ( 9 ( - 8 z 4 ( z - 5 ) + 10 2 1 - z 4 tan - 1 ( 1 - z 4 2 1 - z 4 , - z 4 2 1 - z 4 ) + 10 2 1 - z 4 tan - 1 ( z 4 2 1 - z 4 + 1 , - z 4 2 1 - z 4 ) + 5 2 1 - z 4 log ( z 1 - z - 2 z 4 1 - z 4 + 1 ) - 5 2 1 - z 4 log ( z 1 - z + 2 z 4 1 - z 4 + 1 ) ) ) HypergeometricPFQ 1 2 13 4 z 1 32 z 9 4 -1 9 -8 z 1 4 z -5 10 2 1 2 1 -1 z 1 4 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 10 2 1 2 1 -1 z 1 4 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 5 2 1 2 1 -1 z 1 4 z 1 2 1 -1 z 1 2 -1 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 -1 5 2 1 2 1 -1 z 1 4 z 1 2 1 -1 z 1 2 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List["1", ",", "2", ",", FractionBox["13", "4"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["9", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "8"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "+", "z"]], ")"]], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "+", RowBox[List["10", " ", SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], " ", 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["10", " ", SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], " ", 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["5", " ", SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], " ", 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["5", " ", SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], " ", 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["32", " ", SuperscriptBox["z", RowBox[List["9", "/", "4"]]]]]]]]]]

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

 2007-05-02