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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.b1ac.01

 Input Form

 Hypergeometric2F1[2, 6, 17/5, z] == (7 (1092 - 3120 z + 9025 z^2 - 7000 z^3 + 1875 z^4))/ (78125 (-1 + z)^4 z^2) + (1092 Sqrt[10 - 2 Sqrt[5]] (-1 + z)^4 (-7 + 25 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))])/ (390625 (1 - z)^(43/5) z^(12/5)) - (1092 Sqrt[2 (5 + Sqrt[5])] (-1 + z)^4 (-7 + 25 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))])/ (390625 (1 - z)^(43/5) z^(12/5)) - (2184 (-1 + z)^4 (-7 + 25 z) Log[1 + z^(1/5)/(1 - z)^(1/5)])/ (390625 (1 - z)^(43/5) z^(12/5)) + (546 (1 + Sqrt[5]) (-1 + z)^4 (-7 + 25 z) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(390625 (1 - z)^(43/5) z^(12/5)) - (546 (-1 + Sqrt[5]) (-1 + z)^4 (-7 + 25 z) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(390625 (1 - z)^(43/5) z^(12/5))

 Standard Form

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 MathML Form

 2 F 1 ( 2 , 6 ; 17 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["6", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["17", "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] 1092 10 - 2 5 ( 25 z - 7 ) tan - 1 ( 1 - ( 1 - 5 ) z 5 4 1 - z 5 , - 5 8 + 5 8 z 5 1 - z 5 ) ( z - 1 ) 4 390625 ( 1 - z ) 43 / 5 z 12 / 5 - 1092 2 ( 5 + 5 ) ( 25 z - 7 ) tan - 1 ( 1 - ( 1 + 5 ) z 5 4 1 - z 5 , - 5 8 - 5 8 z 5 1 - z 5 ) ( z - 1 ) 4 390625 ( 1 - z ) 43 / 5 z 12 / 5 - 2184 ( 25 z - 7 ) log ( z 5 1 - z 5 + 1 ) ( z - 1 ) 4 390625 ( 1 - z ) 43 / 5 z 12 / 5 + 546 ( 1 + 5 ) ( 25 z - 7 ) log ( z 2 / 5 ( 1 - z ) 2 / 5 - ( 1 - 5 ) z 5 2 1 - z 5 + 1 ) ( z - 1 ) 4 390625 ( 1 - z ) 43 / 5 z 12 / 5 - 546 ( - 1 + 5 ) ( 25 z - 7 ) log ( z 2 / 5 ( 1 - z ) 2 / 5 - ( 1 + 5 ) z 5 2 1 - z 5 + 1 ) ( z - 1 ) 4 390625 ( 1 - z ) 43 / 5 z 12 / 5 + 7 ( 1875 z 4 - 7000 z 3 + 9025 z 2 - 3120 z + 1092 ) 78125 z 2 ( z - 1 ) 4 HypergeometricPFQ 2 6 17 5 z 1092 10 -1 2 5 1 2 1 2 25 z -7 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 4 390625 1 -1 z 43 5 z 12 5 -1 -1 1092 2 5 5 1 2 1 2 25 z -7 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 4 390625 1 -1 z 43 5 z 12 5 -1 -1 2184 25 z -7 z 1 5 1 -1 z 1 5 -1 1 z -1 4 390625 1 -1 z 43 5 z 12 5 -1 546 1 5 1 2 25 z -7 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 4 390625 1 -1 z 43 5 z 12 5 -1 -1 546 -1 5 1 2 25 z -7 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 4 390625 1 -1 z 43 5 z 12 5 -1 7 1875 z 4 -1 7000 z 3 9025 z 2 -1 3120 z 1092 78125 z 2 z -1 4 -1 [/itex]

 Rule Form

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

 2007-05-02