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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.b16t.01

 Input Form

 Hypergeometric2F1[2, 5, 28/5, z] == (69 (-936 + 455 z + 200 z^2 + 125 z^3))/(6250 (-1 + z) z^4) + (5382 Sqrt[10 - 2 Sqrt[5]] (-1 + z)^8 (-9 + 10 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)^(47/5) z^(23/5)) - (5382 Sqrt[2 (5 + Sqrt[5])] (-1 + z)^8 (-9 + 10 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)^(47/5) z^(23/5)) + (10764 (-1 + z)^8 (-9 + 10 z) Log[1 + z^(1/5)/(1 - z)^(1/5)])/ (15625 (1 - z)^(47/5) z^(23/5)) - (2691 (1 + Sqrt[5]) (-1 + z)^8 (-9 + 10 z) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(15625 (1 - z)^(47/5) z^(23/5)) + (2691 (-1 + Sqrt[5]) (-1 + z)^8 (-9 + 10 z) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(15625 (1 - z)^(47/5) z^(23/5))

 Standard Form

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 MathML Form

 2 F 1 ( 2 , 5 ; 28 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["28", "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] 5382 10 - 2 5 ( 10 z - 9 ) tan - 1 ( 1 - ( 1 - 5 ) z 5 4 1 - z 5 , - 5 8 + 5 8 z 5 1 - z 5 ) ( z - 1 ) 8 15625 ( 1 - z ) 47 / 5 z 23 / 5 - 5382 2 ( 5 + 5 ) ( 10 z - 9 ) tan - 1 ( 1 - ( 1 + 5 ) z 5 4 1 - z 5 , - 5 8 - 5 8 z 5 1 - z 5 ) ( z - 1 ) 8 15625 ( 1 - z ) 47 / 5 z 23 / 5 + 10764 ( 10 z - 9 ) log ( z 5 1 - z 5 + 1 ) ( z - 1 ) 8 15625 ( 1 - z ) 47 / 5 z 23 / 5 - 2691 ( 1 + 5 ) ( 10 z - 9 ) log ( z 2 / 5 ( 1 - z ) 2 / 5 - ( 1 - 5 ) z 5 2 1 - z 5 + 1 ) ( z - 1 ) 8 15625 ( 1 - z ) 47 / 5 z 23 / 5 + 2691 ( - 1 + 5 ) ( 10 z - 9 ) log ( z 2 / 5 ( 1 - z ) 2 / 5 - ( 1 + 5 ) z 5 2 1 - z 5 + 1 ) ( z - 1 ) 8 15625 ( 1 - z ) 47 / 5 z 23 / 5 + 69 ( 125 z 3 + 200 z 2 + 455 z - 936 ) 6250 z 4 ( z - 1 ) HypergeometricPFQ 2 5 28 5 z 5382 10 -1 2 5 1 2 1 2 10 z -9 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 8 15625 1 -1 z 47 5 z 23 5 -1 -1 5382 2 5 5 1 2 1 2 10 z -9 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 8 15625 1 -1 z 47 5 z 23 5 -1 10764 10 z -9 z 1 5 1 -1 z 1 5 -1 1 z -1 8 15625 1 -1 z 47 5 z 23 5 -1 -1 2691 1 5 1 2 10 z -9 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 8 15625 1 -1 z 47 5 z 23 5 -1 2691 -1 5 1 2 10 z -9 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 8 15625 1 -1 z 47 5 z 23 5 -1 69 125 z 3 200 z 2 455 z -936 6250 z 4 z -1 -1 [/itex]

 Rule Form

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

 2007-05-02