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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[1, 1, 19/4, z] == (1/(616 z^(15/4))) (5 (8 z^(3/4) (77 - 187 z + 131 z^2) + 462 Sqrt[2] (1 - z)^(11/4) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] + 462 Sqrt[2] (1 - z)^(11/4) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 231 Sqrt[2] (1 - z)^(11/4) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]] + 231 Sqrt[2] (1 - z)^(11/4) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]]))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["1", ",", "1", ",", FractionBox["19", "4"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["616", " ", SuperscriptBox["z", RowBox[List["15", "/", "4"]]]]]], RowBox[List["(", RowBox[List["5", " ", RowBox[List["(", RowBox[List[RowBox[List["8", " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]], " ", RowBox[List["(", RowBox[List["77", "-", RowBox[List["187", " ", "z"]], "+", RowBox[List["131", " ", SuperscriptBox["z", "2"]]]]], ")"]]]], "+", RowBox[List["462", " ", SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["11", "/", "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["462", " ", SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["11", "/", "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["231", " ", SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["11", "/", "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["231", " ", SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["11", "/", "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"]]]]]], "]"]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( 1 , 1 ; 19 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["1", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["19", "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] 1 616 z 15 / 4 ( 5 ( 462 2 tan - 1 ( 1 - z 4 2 1 - z 4 , - z 4 2 1 - z 4 ) ( 1 - z ) 11 / 4 + 462 2 tan - 1 ( z 4 2 1 - z 4 + 1 , - z 4 2 1 - z 4 ) ( 1 - z ) 11 / 4 - 231 2 log ( z 1 - z - 2 z 4 1 - z 4 + 1 ) ( 1 - z ) 11 / 4 + 231 2 log ( z 1 - z + 2 z 4 1 - z 4 + 1 ) ( 1 - z ) 11 / 4 + 8 z 3 / 4 ( 131 z 2 - 187 z + 77 ) ) ) HypergeometricPFQ 1 1 19 4 z 1 616 z 15 4 -1 5 462 2 1 2 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 11 4 462 2 1 2 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 11 4 -1 231 2 1 2 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 11 4 231 2 1 2 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 11 4 8 z 3 4 131 z 2 -1 187 z 77 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List["1", ",", "1", ",", FractionBox["19", "4"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["5", " ", RowBox[List["(", RowBox[List[RowBox[List["8", " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]], " ", RowBox[List["(", RowBox[List["77", "-", RowBox[List["187", " ", "z"]], "+", RowBox[List["131", " ", SuperscriptBox["z", "2"]]]]], ")"]]]], "+", RowBox[List["462", " ", SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["11", "/", "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["462", " ", SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["11", "/", "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["231", " ", SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["11", "/", "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["231", " ", SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["11", "/", "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["616", " ", SuperscriptBox["z", RowBox[List["15", "/", "4"]]]]]]]]]]

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

 2007-05-02