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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.am2u.01

 Input Form

 Hypergeometric2F1[3, 4, -(1/4), z] == (1/32768) ((8 (-4096 + 225280 z + 1029883 z^2 + 483068 z^3 + 6240 z^4))/ (-1 + z)^7 + (19890 Sqrt[2] z^(5/4) (39 + 104 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)^(29/4) + (19890 Sqrt[2] z^(5/4) (39 + 104 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)^(29/4) - (9945 Sqrt[2] z^(5/4) (39 + 104 z + 32 z^2) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/ (1 - z)^(29/4) + (9945 Sqrt[2] z^(5/4) (39 + 104 z + 32 z^2) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/ (1 - z)^(29/4))

 Standard Form

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 MathML Form

 2 F 1 ( 3 , 4 ; - 1 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["4", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["-", FractionBox["1", "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 32768 ( 19890 2 ( 32 z 2 + 104 z + 39 ) tan - 1 ( 1 - z 4 2 1 - z 4 , - z 4 2 1 - z 4 ) z 5 / 4 ( 1 - z ) 29 / 4 + 19890 2 ( 32 z 2 + 104 z + 39 ) tan - 1 ( z 4 2 1 - z 4 + 1 , - z 4 2 1 - z 4 ) z 5 / 4 ( 1 - z ) 29 / 4 - 9945 2 ( 32 z 2 + 104 z + 39 ) log ( z 1 - z - 2 z 4 1 - z 4 + 1 ) z 5 / 4 ( 1 - z ) 29 / 4 + 9945 2 ( 32 z 2 + 104 z + 39 ) log ( z 1 - z + 2 z 4 1 - z 4 + 1 ) z 5 / 4 ( 1 - z ) 29 / 4 + 8 ( 6240 z 4 + 483068 z 3 + 1029883 z 2 + 225280 z - 4096 ) ( z - 1 ) 7 ) HypergeometricPFQ 3 4 -1 1 4 z 1 32768 19890 2 1 2 32 z 2 104 z 39 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 z 5 4 1 -1 z 29 4 -1 19890 2 1 2 32 z 2 104 z 39 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 z 5 4 1 -1 z 29 4 -1 -1 9945 2 1 2 32 z 2 104 z 39 z 1 2 1 -1 z 1 2 -1 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 z 5 4 1 -1 z 29 4 -1 9945 2 1 2 32 z 2 104 z 39 z 1 2 1 -1 z 1 2 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 z 5 4 1 -1 z 29 4 -1 8 6240 z 4 483068 z 3 1029883 z 2 225280 z -4096 z -1 7 -1 [/itex]

 Rule Form

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

 2007-05-02