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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.b16h.01

 Input Form

 Hypergeometric2F1[2, 5, 13/5, z] == (2 (84 + 1055 z - 550 z^2 + 125 z^3))/(3125 (-1 + z)^4 z) + (84 Sqrt[10 - 2 Sqrt[5]] (-1 + z)^2 (-3 + 20 z) 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)^(32/5) z^(8/5)) - (84 Sqrt[2 (5 + Sqrt[5])] (-1 + z)^2 (-3 + 20 z) 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)^(32/5) z^(8/5)) + (168 (-1 + z)^2 (-3 + 20 z) Log[1 + z^(1/5)/(1 - z)^(1/5)])/ (15625 (1 - z)^(32/5) z^(8/5)) - (42 (1 + Sqrt[5]) (-1 + z)^2 (-3 + 20 z) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(15625 (1 - z)^(32/5) z^(8/5)) + (42 (-1 + Sqrt[5]) (-1 + z)^2 (-3 + 20 z) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(15625 (1 - z)^(32/5) z^(8/5))

 Standard Form

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 MathML Form

 2 F 1 ( 2 , 5 ; 13 5 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["2", 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["13", "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] 84 10 - 2 5 ( 20 z - 3 ) 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 ) 32 / 5 z 8 / 5 - 84 2 ( 5 + 5 ) ( 20 z - 3 ) 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 ) 32 / 5 z 8 / 5 + 168 ( 20 z - 3 ) log ( z 5 1 - z 5 + 1 ) ( z - 1 ) 2 15625 ( 1 - z ) 32 / 5 z 8 / 5 - 42 ( 1 + 5 ) ( 20 z - 3 ) log ( z 2 / 5 ( 1 - z ) 2 / 5 - ( 1 - 5 ) z 5 2 1 - z 5 + 1 ) ( z - 1 ) 2 15625 ( 1 - z ) 32 / 5 z 8 / 5 + 42 ( - 1 + 5 ) ( 20 z - 3 ) log ( z 2 / 5 ( 1 - z ) 2 / 5 - ( 1 + 5 ) z 5 2 1 - z 5 + 1 ) ( z - 1 ) 2 15625 ( 1 - z ) 32 / 5 z 8 / 5 + 2 ( 125 z 3 - 550 z 2 + 1055 z + 84 ) 3125 z ( z - 1 ) 4 HypergeometricPFQ 2 5 13 5 z 84 10 -1 2 5 1 2 1 2 20 z -3 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 32 5 z 8 5 -1 -1 84 2 5 5 1 2 1 2 20 z -3 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 32 5 z 8 5 -1 168 20 z -3 z 1 5 1 -1 z 1 5 -1 1 z -1 2 15625 1 -1 z 32 5 z 8 5 -1 -1 42 1 5 1 2 20 z -3 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 32 5 z 8 5 -1 42 -1 5 1 2 20 z -3 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 32 5 z 8 5 -1 2 125 z 3 -1 550 z 2 1055 z 84 3125 z z -1 4 -1 [/itex]

 Rule Form

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

 2007-05-02