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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.b19d.01

 Input Form

 Hypergeometric2F1[2, 6, -(27/5), z] == (67108864 ((1 - z)^(4/5) - (1 - z)^(3/5) z^(1/5) + (1 - z)^(2/5) z^(2/5) - (1 - z)^(1/5) z^(3/5) + z^(4/5))^12 (-131484375 + 2001484375 z - 14751484375 z^2 + 71647109375 z^3 - 270655078125 z^4 + 969368828125 z^5 - 6488049453125 z^6 - 8827431246643 z^7 - 555300397080 z^8 + 59244629400 z^9 - 5791203000 z^10 + 311355000 z^11))/ (131484375 ((1 - z)^(1/5) + z^(1/5)) (2 (1 - z)^(2/5) + (-1 + Sqrt[5]) (1 - z)^(1/5) z^(1/5) + 2 z^(2/5))^13 (2 (1 - z)^(2/5) - (1 + Sqrt[5]) (1 - z)^(1/5) z^(1/5) + 2 z^(2/5))^13 (-1 + z)^13) + (144323088 Sqrt[10 - 2 Sqrt[5]] z^(32/5) (37 + 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)^(67/5)) - (144323088 Sqrt[2 (5 + Sqrt[5])] z^(32/5) (37 + 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)^(67/5)) + (288646176 z^(32/5) (37 + 25 z) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(390625 (1 - z)^(67/5)) - (72161544 (1 + Sqrt[5]) z^(32/5) (37 + 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)^(67/5)) + (72161544 (-1 + Sqrt[5]) z^(32/5) (37 + 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)^(67/5))

 Standard Form

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 MathML Form

 2 F 1 ( 2 , 6 ; - 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["6", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["-", 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] ( 67108864 ( 311355000 z 11 - 5791203000 z 10 + 59244629400 z 9 - 555300397080 z 8 - 8827431246643 z 7 - 6488049453125 z 6 + 969368828125 z 5 - 270655078125 z 4 + 71647109375 z 3 - 14751484375 z 2 + 2001484375 z - 131484375 ) ( ( 1 - z ) 4 / 5 - z 5 ( 1 - z ) 3 / 5 + z 2 / 5 ( 1 - z ) 2 / 5 - z 3 / 5 1 - z 5 + z 4 / 5 ) 12 ) / ( 131484375 ( 1 - z 5 + z 5 ) ( 2 ( 1 - z ) 2 / 5 + ( - 1 + 5 ) z 5 1 - z 5 + 2 z 2 / 5 ) 13 ( 2 ( 1 - z ) 2 / 5 - ( 1 + 5 ) z 5 1 - z 5 + 2 z 2 / 5 ) 13 ( z - 1 ) 13 ) + 144323088 10 - 2 5 z 32 / 5 ( 25 z + 37 ) tan - 1 ( 1 - ( 1 - 5 ) z 5 4 1 - z 5 , - 5 8 + 5 8 z 5 1 - z 5 ) 390625 ( 1 - z ) 67 / 5 - 144323088 2 ( 5 + 5 ) z 32 / 5 ( 25 z + 37 ) tan - 1 ( 1 - ( 1 + 5 ) z 5 4 1 - z 5 , - 5 8 - 5 8 z 5 1 - z 5 ) 390625 ( 1 - z ) 67 / 5 + 288646176 z 32 / 5 ( 25 z + 37 ) log ( z 5 1 - z 5 + 1 ) 390625 ( 1 - z ) 67 / 5 - 72161544 ( 1 + 5 ) z 32 / 5 ( 25 z + 37 ) log ( z 2 / 5 ( 1 - z ) 2 / 5 - ( 1 - 5 ) z 5 2 1 - z 5 + 1 ) 390625 ( 1 - z ) 67 / 5 + 72161544 ( - 1 + 5 ) z 32 / 5 ( 25 z + 37 ) log ( z 2 / 5 ( 1 - z ) 2 / 5 - ( 1 + 5 ) z 5 2 1 - z 5 + 1 ) 390625 ( 1 - z ) 67 / 5 HypergeometricPFQ 2 6 -1 27 5 z 67108864 311355000 z 11 -1 5791203000 z 10 59244629400 z 9 -1 555300397080 z 8 -1 8827431246643 z 7 -1 6488049453125 z 6 969368828125 z 5 -1 270655078125 z 4 71647109375 z 3 -1 14751484375 z 2 2001484375 z -131484375 1 -1 z 4 5 -1 z 1 5 1 -1 z 3 5 z 2 5 1 -1 z 2 5 -1 z 3 5 1 -1 z 1 5 z 4 5 12 131484375 1 -1 z 1 5 z 1 5 2 1 -1 z 2 5 -1 5 1 2 z 1 5 1 -1 z 1 5 2 z 2 5 13 2 1 -1 z 2 5 -1 1 5 1 2 z 1 5 1 -1 z 1 5 2 z 2 5 13 z -1 13 -1 144323088 10 -1 2 5 1 2 1 2 z 32 5 25 z 37 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 390625 1 -1 z 67 5 -1 -1 144323088 2 5 5 1 2 1 2 z 32 5 25 z 37 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 390625 1 -1 z 67 5 -1 288646176 z 32 5 25 z 37 z 1 5 1 -1 z 1 5 -1 1 390625 1 -1 z 67 5 -1 -1 72161544 1 5 1 2 z 32 5 25 z 37 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 390625 1 -1 z 67 5 -1 72161544 -1 5 1 2 z 32 5 25 z 37 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 390625 1 -1 z 67 5 -1 [/itex]

 Rule Form

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

 2007-05-02