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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.al20.01

 Input Form

 Hypergeometric2F1[2, 6, 7/4, z] == (1/1310720) ((8 (160525 + 72240 z - 32880 z^2 + 10496 z^3 - 1536 z^4))/ (-1 + z)^6 - (19890 Sqrt[2] (1 + 20 z) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/((1 - z)^(25/4) z^(3/4)) - (19890 Sqrt[2] (1 + 20 z) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/((1 - z)^(25/4) z^(3/4)) + (9945 Sqrt[2] (1 + 20 z) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/((1 - z)^(25/4) z^(3/4)) - (9945 Sqrt[2] (1 + 20 z) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/((1 - z)^(25/4) z^(3/4)))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["2", ",", "6", ",", FractionBox["7", "4"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "1310720"], RowBox[List["(", RowBox[List[FractionBox[RowBox[List["8", " ", RowBox[List["(", RowBox[List["160525", "+", RowBox[List["72240", " ", "z"]], "-", RowBox[List["32880", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["10496", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1536", " ", SuperscriptBox["z", "4"]]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "6"]], "-", FractionBox[RowBox[List["19890", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["20", " ", "z"]]]], ")"]], " ", 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["25", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]]]]], "-", FractionBox[RowBox[List["19890", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["20", " ", "z"]]]], ")"]], " ", 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["25", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]]]]], "+", FractionBox[RowBox[List["9945", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["20", " ", "z"]]]], ")"]], " ", 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["25", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]]]]], "-", FractionBox[RowBox[List["9945", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["20", " ", "z"]]]], ")"]], " ", 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["25", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]]]]]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( 2 , 6 ; 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["2", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["6", 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 1310720 ( 8 ( - 1536 z 4 + 10496 z 3 - 32880 z 2 + 72240 z + 160525 ) ( z - 1 ) 6 - 19890 2 ( 20 z + 1 ) tan - 1 ( 1 - z 4 2 1 - z 4 , - z 4 2 1 - z 4 ) ( 1 - z ) 25 / 4 z 3 / 4 - 19890 2 ( 20 z + 1 ) tan - 1 ( z 4 2 1 - z 4 + 1 , - z 4 2 1 - z 4 ) ( 1 - z ) 25 / 4 z 3 / 4 + 9945 2 ( 20 z + 1 ) log ( z 1 - z - 2 z 4 1 - z 4 + 1 ) ( 1 - z ) 25 / 4 z 3 / 4 - 9945 2 ( 20 z + 1 ) log ( z 1 - z + 2 z 4 1 - z 4 + 1 ) ( 1 - z ) 25 / 4 z 3 / 4 ) HypergeometricPFQ 2 6 7 4 z 1 1310720 8 -1536 z 4 10496 z 3 -1 32880 z 2 72240 z 160525 z -1 6 -1 -1 19890 2 1 2 20 z 1 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 25 4 z 3 4 -1 -1 19890 2 1 2 20 z 1 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 25 4 z 3 4 -1 9945 2 1 2 20 z 1 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 25 4 z 3 4 -1 -1 9945 2 1 2 20 z 1 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 25 4 z 3 4 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List["2", ",", "6", ",", FractionBox["7", "4"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[FractionBox[RowBox[List["8", " ", RowBox[List["(", RowBox[List["160525", "+", RowBox[List["72240", " ", "z"]], "-", RowBox[List["32880", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["10496", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1536", " ", SuperscriptBox["z", "4"]]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "6"]], "-", FractionBox[RowBox[List["19890", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["20", " ", "z"]]]], ")"]], " ", 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["25", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]]]]], "-", FractionBox[RowBox[List["19890", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["20", " ", "z"]]]], ")"]], " ", 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["25", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]]]]], "+", FractionBox[RowBox[List["9945", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["20", " ", "z"]]]], ")"]], " ", 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["25", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]]]]], "-", FractionBox[RowBox[List["9945", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["20", " ", "z"]]]], ")"]], " ", 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["25", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]]]]]]], "1310720"]]]]]

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

 2007-05-02