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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[4, 4, 3/4, z] == (1/393216) (-((8 (49152 + 666487 z + 886480 z^2 + 138256 z^3))/(-1 + z)^7) - (1/(1 - z)^(29/4)) (1170 Sqrt[2] z^(1/4) (195 + 1404 z + 1248 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/(1 - z)^(29/4)) (1170 Sqrt[2] z^(1/4) (195 + 1404 z + 1248 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)))]) + (585 Sqrt[2] z^(1/4) (195 + 1404 z + 1248 z^2 + 128 z^3) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/ (1 - z)^(29/4) - (585 Sqrt[2] z^(1/4) (195 + 1404 z + 1248 z^2 + 128 z^3) 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 ( 4 , 4 ; 3 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["3", "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 393216 ( - 8 ( 138256 z 3 + 886480 z 2 + 666487 z + 49152 ) ( z - 1 ) 7 - 1170 2 z 4 ( 128 z 3 + 1248 z 2 + 1404 z + 195 ) tan - 1 ( 1 - z 4 2 1 - z 4 , - z 4 2 1 - z 4 ) ( 1 - z ) 29 / 4 - 1170 2 z 4 ( 128 z 3 + 1248 z 2 + 1404 z + 195 ) tan - 1 ( z 4 2 1 - z 4 + 1 , - z 4 2 1 - z 4 ) ( 1 - z ) 29 / 4 + 585 2 z 4 ( 128 z 3 + 1248 z 2 + 1404 z + 195 ) log ( z 1 - z - 2 z 4 1 - z 4 + 1 ) ( 1 - z ) 29 / 4 - 585 2 z 4 ( 128 z 3 + 1248 z 2 + 1404 z + 195 ) log ( z 1 - z + 2 z 4 1 - z 4 + 1 ) ( 1 - z ) 29 / 4 ) HypergeometricPFQ 4 4 3 4 z 1 393216 -1 8 138256 z 3 886480 z 2 666487 z 49152 z -1 7 -1 -1 1170 2 1 2 z 1 4 128 z 3 1248 z 2 1404 z 195 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 29 4 -1 -1 1170 2 1 2 z 1 4 128 z 3 1248 z 2 1404 z 195 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 29 4 -1 585 2 1 2 z 1 4 128 z 3 1248 z 2 1404 z 195 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 29 4 -1 -1 585 2 1 2 z 1 4 128 z 3 1248 z 2 1404 z 195 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 29 4 -1 [/itex]

 Rule Form

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

 2007-05-02