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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.b2g7.01

 Input Form

 Hypergeometric2F1[3, 4, -(9/5), z] == (9375 - 137500 z + 1543750 z^2 + 9431996 z^3 + 4415725 z^4 + 79800 z^5)/ (9375 (-1 + z)^8) - (1/(15625 (1 - z)^(44/5))) (46284 Sqrt[2 (5 + Sqrt[5])] z^(14/5) (76 + 120 z + 25 z^2) ArcTan[1 - ((1 - Sqrt[5]) z^(1/5))/(4 (1 - z)^(1/5)), -((Sqrt[5/8 + Sqrt[5]/8] z^(1/5))/(1 - z)^(1/5))]) - (1/(15625 (1 - z)^(44/5))) (46284 Sqrt[10 - 2 Sqrt[5]] z^(14/5) (76 + 120 z + 25 z^2) ArcTan[1 - ((1 + Sqrt[5]) z^(1/5))/ (4 (1 - z)^(1/5)), -((Sqrt[5/8 - Sqrt[5]/8] z^(1/5))/ (1 - z)^(1/5))]) + (92568 z^(14/5) (76 + 120 z + 25 z^2) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(15625 (1 - z)^(44/5)) + (23142 (-1 + Sqrt[5]) z^(14/5) (76 + 120 z + 25 z^2) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(15625 (1 - z)^(44/5)) - (23142 (1 + Sqrt[5]) z^(14/5) (76 + 120 z + 25 z^2) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(15625 (1 - z)^(44/5))

 Standard Form

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 MathML Form

 2 F 1 ( 3 , 4 ; - 9 5 ; 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["9", "5"]]], 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] - 46284 2 ( 5 + 5 ) ( 25 z 2 + 120 z + 76 ) tan - 1 ( 1 - ( 1 - 5 ) z 5 4 1 - z 5 , - 5 8 + 5 8 z 5 1 - z 5 ) z 14 / 5 15625 ( 1 - z ) 44 / 5 - 46284 10 - 2 5 ( 25 z 2 + 120 z + 76 ) tan - 1 ( 1 - ( 1 + 5 ) z 5 4 1 - z 5 , - 5 8 - 5 8 z 5 1 - z 5 ) z 14 / 5 15625 ( 1 - z ) 44 / 5 + 92568 ( 25 z 2 + 120 z + 76 ) log ( z 5 1 - z 5 + 1 ) z 14 / 5 15625 ( 1 - z ) 44 / 5 + 23142 ( - 1 + 5 ) ( 25 z 2 + 120 z + 76 ) log ( z 2 / 5 ( 1 - z ) 2 / 5 - ( 1 - 5 ) z 5 2 1 - z 5 + 1 ) z 14 / 5 15625 ( 1 - z ) 44 / 5 - 23142 ( 1 + 5 ) ( 25 z 2 + 120 z + 76 ) log ( z 2 / 5 ( 1 - z ) 2 / 5 - ( 1 + 5 ) z 5 2 1 - z 5 + 1 ) z 14 / 5 15625 ( 1 - z ) 44 / 5 + 79800 z 5 + 4415725 z 4 + 9431996 z 3 + 1543750 z 2 - 137500 z + 9375 9375 ( z - 1 ) 8 HypergeometricPFQ 3 4 -1 9 5 z -1 46284 2 5 5 1 2 1 2 25 z 2 120 z 76 1 -1 1 -1 5 1 2 z 1 5 4 1 -1 z 1 5 -1 -1 5 8 5 1 2 8 -1 1 2 z 1 5 1 -1 z 1 5 -1 z 14 5 15625 1 -1 z 44 5 -1 -1 46284 10 -1 2 5 1 2 1 2 25 z 2 120 z 76 1 -1 1 5 1 2 z 1 5 4 1 -1 z 1 5 -1 -1 5 8 -1 5 1 2 8 -1 1 2 z 1 5 1 -1 z 1 5 -1 z 14 5 15625 1 -1 z 44 5 -1 92568 25 z 2 120 z 76 z 1 5 1 -1 z 1 5 -1 1 z 14 5 15625 1 -1 z 44 5 -1 23142 -1 5 1 2 25 z 2 120 z 76 z 2 5 1 -1 z 2 5 -1 -1 1 -1 5 1 2 z 1 5 2 1 -1 z 1 5 -1 1 z 14 5 15625 1 -1 z 44 5 -1 -1 23142 1 5 1 2 25 z 2 120 z 76 z 2 5 1 -1 z 2 5 -1 -1 1 5 1 2 z 1 5 2 1 -1 z 1 5 -1 1 z 14 5 15625 1 -1 z 44 5 -1 79800 z 5 4415725 z 4 9431996 z 3 1543750 z 2 -1 137500 z 9375 9375 z -1 8 -1 [/itex]

 Rule Form

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

 2007-05-02