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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[4, 5, 3/4, z] == (1/6291456) ((8 (786432 + 14033639 z + 27428756 z^2 + 8147168 z^3 + 74880 z^4))/(-1 + z)^8 - (1/(1 - z)^(33/4)) (19890 Sqrt[2] z^(1/4) (195 + 1872 z + 2496 z^2 + 512 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)^(33/4)) (19890 Sqrt[2] z^(1/4) (195 + 1872 z + 2496 z^2 + 512 z^3) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))]) + (9945 Sqrt[2] z^(1/4) (195 + 1872 z + 2496 z^2 + 512 z^3) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/ (1 - z)^(33/4) - (9945 Sqrt[2] z^(1/4) (195 + 1872 z + 2496 z^2 + 512 z^3) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/(1 - z)^(33/4))

 Standard Form

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 MathML Form

 2 F 1 ( 4 , 5 ; 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["5", 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 6291456 ( 8 ( 74880 z 4 + 8147168 z 3 + 27428756 z 2 + 14033639 z + 786432 ) ( z - 1 ) 8 - 19890 2 z 4 ( 512 z 3 + 2496 z 2 + 1872 z + 195 ) tan - 1 ( 1 - z 4 2 1 - z 4 , - z 4 2 1 - z 4 ) ( 1 - z ) 33 / 4 - 19890 2 z 4 ( 512 z 3 + 2496 z 2 + 1872 z + 195 ) tan - 1 ( z 4 2 1 - z 4 + 1 , - z 4 2 1 - z 4 ) ( 1 - z ) 33 / 4 + 9945 2 z 4 ( 512 z 3 + 2496 z 2 + 1872 z + 195 ) log ( z 1 - z - 2 z 4 1 - z 4 + 1 ) ( 1 - z ) 33 / 4 - 9945 2 z 4 ( 512 z 3 + 2496 z 2 + 1872 z + 195 ) log ( z 1 - z + 2 z 4 1 - z 4 + 1 ) ( 1 - z ) 33 / 4 ) HypergeometricPFQ 4 5 3 4 z 1 6291456 8 74880 z 4 8147168 z 3 27428756 z 2 14033639 z 786432 z -1 8 -1 -1 19890 2 1 2 z 1 4 512 z 3 2496 z 2 1872 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 33 4 -1 -1 19890 2 1 2 z 1 4 512 z 3 2496 z 2 1872 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 33 4 -1 9945 2 1 2 z 1 4 512 z 3 2496 z 2 1872 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 33 4 -1 -1 9945 2 1 2 z 1 4 512 z 3 2496 z 2 1872 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 33 4 -1 [/itex]

 Rule Form

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

 2007-05-02