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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.b2gu.01

 Input Form

 Hypergeometric2F1[3, 4, 19/5, z] == -((42 (-9 + 25 z + 50 z^2))/(3125 (-1 + z)^3 z^2)) - (126 Sqrt[2 (5 + Sqrt[5])] (-1 + z)^2 (6 - 20 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))])/ (15625 (1 - z)^(26/5) z^(14/5)) - (126 Sqrt[10 - 2 Sqrt[5]] (-1 + z)^2 (6 - 20 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))])/ (15625 (1 - z)^(26/5) z^(14/5)) - (252 (-1 + z)^2 (6 - 20 z + 25 z^2) Log[1 + z^(1/5)/(1 - z)^(1/5)])/ (15625 (1 - z)^(26/5) z^(14/5)) - (63 (-1 + Sqrt[5]) (-1 + z)^2 (6 - 20 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)^(26/5) z^(14/5)) + (63 (1 + Sqrt[5]) (-1 + z)^2 (6 - 20 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)^(26/5) z^(14/5))

 Standard Form

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 MathML Form

 2 F 1 ( 3 , 4 ; 19 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[FractionBox["19", "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] - 126 2 ( 5 + 5 ) ( 25 z 2 - 20 z + 6 ) tan - 1 ( 1 - ( 1 - 5 ) z 5 4 1 - z 5 , - 5 8 + 5 8 z 5 1 - z 5 ) ( z - 1 ) 2 15625 ( 1 - z ) 26 / 5 z 14 / 5 - 126 10 - 2 5 ( 25 z 2 - 20 z + 6 ) tan - 1 ( 1 - ( 1 + 5 ) z 5 4 1 - z 5 , - 5 8 - 5 8 z 5 1 - z 5 ) ( z - 1 ) 2 15625 ( 1 - z ) 26 / 5 z 14 / 5 - 252 ( 25 z 2 - 20 z + 6 ) log ( z 5 1 - z 5 + 1 ) ( z - 1 ) 2 15625 ( 1 - z ) 26 / 5 z 14 / 5 - 63 ( - 1 + 5 ) ( 25 z 2 - 20 z + 6 ) log ( z 2 / 5 ( 1 - z ) 2 / 5 - ( 1 - 5 ) z 5 2 1 - z 5 + 1 ) ( z - 1 ) 2 15625 ( 1 - z ) 26 / 5 z 14 / 5 + 63 ( 1 + 5 ) ( 25 z 2 - 20 z + 6 ) log ( z 2 / 5 ( 1 - z ) 2 / 5 - ( 1 + 5 ) z 5 2 1 - z 5 + 1 ) ( z - 1 ) 2 15625 ( 1 - z ) 26 / 5 z 14 / 5 - 42 ( 50 z 2 + 25 z - 9 ) 3125 z 2 ( z - 1 ) 3 HypergeometricPFQ 3 4 19 5 z -1 126 2 5 5 1 2 1 2 25 z 2 -1 20 z 6 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 -1 2 15625 1 -1 z 26 5 z 14 5 -1 -1 126 10 -1 2 5 1 2 1 2 25 z 2 -1 20 z 6 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 -1 2 15625 1 -1 z 26 5 z 14 5 -1 -1 252 25 z 2 -1 20 z 6 z 1 5 1 -1 z 1 5 -1 1 z -1 2 15625 1 -1 z 26 5 z 14 5 -1 -1 63 -1 5 1 2 25 z 2 -1 20 z 6 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 -1 2 15625 1 -1 z 26 5 z 14 5 -1 63 1 5 1 2 25 z 2 -1 20 z 6 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 -1 2 15625 1 -1 z 26 5 z 14 5 -1 -1 42 50 z 2 25 z -9 3125 z 2 z -1 3 -1 [/itex]

 Rule Form

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

 2007-05-02