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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[4, 4, 17/4, z] == (1/(131072 (-1 + z)^3 z^(13/4))) (65 (-8 z^(1/4) (45 - 144 z + 176 z^2) + (6 Sqrt[2] (-15 + 60 z - 96 z^2 + 128 z^3) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(3/4) + (6 Sqrt[2] (-15 + 60 z - 96 z^2 + 128 z^3) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(3/4) + (3 Sqrt[2] (-15 + 60 z - 96 z^2 + 128 z^3) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/ (1 - z)^(3/4) - (3 Sqrt[2] (-15 + 60 z - 96 z^2 + 128 z^3) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/ (1 - z)^(3/4)))

 Standard Form

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 MathML Form

 2 F 1 ( 4 , 4 ; 17 4 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["4", 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[FractionBox["17", "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 131072 ( z - 1 ) 3 z 13 / 4 ( 65 ( - 8 z 4 ( 176 z 2 - 144 z + 45 ) + 6 2 ( 128 z 3 - 96 z 2 + 60 z - 15 ) tan - 1 ( 1 - z 4 2 1 - z 4 , - z 4 2 1 - z 4 ) ( 1 - z ) 3 / 4 + 6 2 ( 128 z 3 - 96 z 2 + 60 z - 15 ) tan - 1 ( z 4 2 1 - z 4 + 1 , - z 4 2 1 - z 4 ) ( 1 - z ) 3 / 4 + 3 2 ( 128 z 3 - 96 z 2 + 60 z - 15 ) log ( z 1 - z - 2 z 4 1 - z 4 + 1 ) ( 1 - z ) 3 / 4 - 3 2 ( 128 z 3 - 96 z 2 + 60 z - 15 ) log ( z 1 - z + 2 z 4 1 - z 4 + 1 ) ( 1 - z ) 3 / 4 ) ) HypergeometricPFQ 4 4 17 4 z 1 131072 z -1 3 z 13 4 -1 65 -8 z 1 4 176 z 2 -1 144 z 45 6 2 1 2 128 z 3 -1 96 z 2 60 z -15 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 3 4 -1 6 2 1 2 128 z 3 -1 96 z 2 60 z -15 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 3 4 -1 3 2 1 2 128 z 3 -1 96 z 2 60 z -15 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 3 4 -1 -1 3 2 1 2 128 z 3 -1 96 z 2 60 z -15 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 3 4 -1 [/itex]

 Rule Form

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

 2007-05-02