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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.b12w.01

 Input Form

 Hypergeometric2F1[2, 4, 22/5, z] == (34 (-84 + 45 z + 25 z^2))/(625 (-1 + z) z^3) + (714 Sqrt[10 - 2 Sqrt[5]] (-1 + z)^6 (-4 + 5 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))])/ (3125 (1 - z)^(38/5) z^(17/5)) - (714 Sqrt[2 (5 + Sqrt[5])] (-1 + z)^6 (-4 + 5 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))])/ (3125 (1 - z)^(38/5) z^(17/5)) - (1428 (-1 + z)^6 (-4 + 5 z) Log[1 + z^(1/5)/(1 - z)^(1/5)])/ (3125 (1 - z)^(38/5) z^(17/5)) + (357 (1 + Sqrt[5]) (-1 + z)^6 (-4 + 5 z) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(3125 (1 - z)^(38/5) z^(17/5)) - (357 (-1 + Sqrt[5]) (-1 + z)^6 (-4 + 5 z) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(3125 (1 - z)^(38/5) z^(17/5))

 Standard Form

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 MathML Form

 2 F 1 ( 2 , 4 ; 22 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["4", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["22", "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] 714 10 - 2 5 ( 5 z - 4 ) tan - 1 ( 1 - ( 1 - 5 ) z 5 4 1 - z 5 , - 5 8 + 5 8 z 5 1 - z 5 ) ( z - 1 ) 6 3125 ( 1 - z ) 38 / 5 z 17 / 5 - 714 2 ( 5 + 5 ) ( 5 z - 4 ) tan - 1 ( 1 - ( 1 + 5 ) z 5 4 1 - z 5 , - 5 8 - 5 8 z 5 1 - z 5 ) ( z - 1 ) 6 3125 ( 1 - z ) 38 / 5 z 17 / 5 - 1428 ( 5 z - 4 ) log ( z 5 1 - z 5 + 1 ) ( z - 1 ) 6 3125 ( 1 - z ) 38 / 5 z 17 / 5 + 357 ( 1 + 5 ) ( 5 z - 4 ) log ( z 2 / 5 ( 1 - z ) 2 / 5 - ( 1 - 5 ) z 5 2 1 - z 5 + 1 ) ( z - 1 ) 6 3125 ( 1 - z ) 38 / 5 z 17 / 5 - 357 ( - 1 + 5 ) ( 5 z - 4 ) log ( z 2 / 5 ( 1 - z ) 2 / 5 - ( 1 + 5 ) z 5 2 1 - z 5 + 1 ) ( z - 1 ) 6 3125 ( 1 - z ) 38 / 5 z 17 / 5 + 34 ( 25 z 2 + 45 z - 84 ) 625 z 3 ( z - 1 ) HypergeometricPFQ 2 4 22 5 z 714 10 -1 2 5 1 2 1 2 5 z -4 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 6 3125 1 -1 z 38 5 z 17 5 -1 -1 714 2 5 5 1 2 1 2 5 z -4 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 6 3125 1 -1 z 38 5 z 17 5 -1 -1 1428 5 z -4 z 1 5 1 -1 z 1 5 -1 1 z -1 6 3125 1 -1 z 38 5 z 17 5 -1 357 1 5 1 2 5 z -4 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 6 3125 1 -1 z 38 5 z 17 5 -1 -1 357 -1 5 1 2 5 z -4 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 6 3125 1 -1 z 38 5 z 17 5 -1 34 25 z 2 45 z -84 625 z 3 z -1 -1 [/itex]

 Rule Form

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

 2007-05-02