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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.b16s.01

 Input Form

 Hypergeometric2F1[2, 5, 27/5, z] == (187 (-714 + 330 z + 175 z^2 + 125 z^3))/(18750 (-1 + z) z^4) + (1309 Sqrt[10 - 2 Sqrt[5]] (-1 + z)^8 (-17 + 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)^(48/5) z^(22/5)) - (1309 Sqrt[2 (5 + Sqrt[5])] (-1 + z)^8 (-17 + 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)^(48/5) z^(22/5)) - (2618 (-1 + z)^8 (-17 + 20 z) Log[1 + z^(1/5)/(1 - z)^(1/5)])/ (15625 (1 - z)^(48/5) z^(22/5)) + (1309 (1 + Sqrt[5]) (-1 + z)^8 (-17 + 20 z) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(31250 (1 - z)^(48/5) z^(22/5)) - (1309 (-1 + Sqrt[5]) (-1 + z)^8 (-17 + 20 z) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(31250 (1 - z)^(48/5) z^(22/5))

 Standard Form

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 MathML Form

 2 F 1 ( 2 , 5 ; 27 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["27", "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] 1309 10 - 2 5 ( 20 z - 17 ) 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 ) 48 / 5 z 22 / 5 - 1309 2 ( 5 + 5 ) ( 20 z - 17 ) 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 ) 48 / 5 z 22 / 5 - 2618 ( 20 z - 17 ) log ( z 5 1 - z 5 + 1 ) ( z - 1 ) 8 15625 ( 1 - z ) 48 / 5 z 22 / 5 + 1309 ( 1 + 5 ) ( 20 z - 17 ) log ( z 2 / 5 ( 1 - z ) 2 / 5 - ( 1 - 5 ) z 5 2 1 - z 5 + 1 ) ( z - 1 ) 8 31250 ( 1 - z ) 48 / 5 z 22 / 5 - 1309 ( - 1 + 5 ) ( 20 z - 17 ) log ( z 2 / 5 ( 1 - z ) 2 / 5 - ( 1 + 5 ) z 5 2 1 - z 5 + 1 ) ( z - 1 ) 8 31250 ( 1 - z ) 48 / 5 z 22 / 5 + 187 ( 125 z 3 + 175 z 2 + 330 z - 714 ) 18750 z 4 ( z - 1 ) HypergeometricPFQ 2 5 27 5 z 1309 10 -1 2 5 1 2 1 2 20 z -17 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 48 5 z 22 5 -1 -1 1309 2 5 5 1 2 1 2 20 z -17 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 48 5 z 22 5 -1 -1 2618 20 z -17 z 1 5 1 -1 z 1 5 -1 1 z -1 8 15625 1 -1 z 48 5 z 22 5 -1 1309 1 5 1 2 20 z -17 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 31250 1 -1 z 48 5 z 22 5 -1 -1 1309 -1 5 1 2 20 z -17 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 31250 1 -1 z 48 5 z 22 5 -1 187 125 z 3 175 z 2 330 z -714 18750 z 4 z -1 -1 [/itex]

 Rule Form

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

 2007-05-02