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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(27/5), 4, -(17/5), -z] == (1/3125) (99 ((25 (79 + 74 z))/(1 + z)^2 - 31968 (-(5/22) + (5 z)/17 - (5 z^2)/12 + (5 z^3)/7 - (5 z^4)/2 - z^(22/5) (Log[1 + z^(1/5)] + (-1)^(2/5) Log[1 - (-1)^(1/5) z^(1/5)] + (-1)^(4/5) Log[1 + (-1)^(2/5) z^(1/5)] - (-1)^(1/5) Log[1 - (-1)^(3/5) z^(1/5)] - (-1)^(3/5) Log[1 + (-1)^(4/5) z^(1/5)])) + 49728 (-(5/27) + (5 z)/22 - (5 z^2)/17 + (5 z^3)/12 - (5 z^4)/7 + (5 z^5)/2 + z^(27/5) (Log[1 + z^(1/5)] + (-1)^(2/5) Log[1 - (-1)^(1/5) z^(1/5)] + (-1)^(4/5) Log[1 + (-1)^(2/5) z^(1/5)] - (-1)^(1/5) Log[1 - (-1)^(3/5) z^(1/5)] - (-1)^(3/5) Log[1 + (-1)^(4/5) z^(1/5)]))))

 Standard Form

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 MathML Form

 2 F 1 ( - 27 5 , 4 ; - 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[RowBox[List["-", FractionBox["27", "5"]]], 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[RowBox[List["-", FractionBox["17", "5"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", "z"]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] 1 3125 ( 99 ( 25 ( 74 z + 79 ) ( z + 1 ) 2 - 31968 ( - ( log ( z 5 + 1 ) + ( - 1 ) 2 / 5 log ( 1 - - 1 5 z 5 ) + ( - 1 ) 4 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) - - 1 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) - ( - 1 ) 3 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) z 22 / 5 - 5 z 4 2 + 5 z 3 7 - 5 z 2 12 + 5 z 17 - 5 22 ) + 49728 ( ( log ( z 5 + 1 ) + ( - 1 ) 2 / 5 log ( 1 - - 1 5 z 5 ) + ( - 1 ) 4 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) - - 1 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) - ( - 1 ) 3 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) z 27 / 5 + 5 z 5 2 - 5 z 4 7 + 5 z 3 12 - 5 z 2 17 + 5 z 22 - 5 27 ) ) ) HypergeometricPFQ -1 27 5 4 -1 17 5 -1 z 1 3125 99 25 74 z 79 z 1 2 -1 -1 31968 -1 z 1 5 1 -1 2 5 1 -1 -1 1 5 z 1 5 -1 4 5 -1 2 5 z 1 5 1 -1 -1 1 5 1 -1 -1 3 5 z 1 5 -1 -1 3 5 -1 4 5 z 1 5 1 z 22 5 -1 5 z 4 2 -1 5 z 3 7 -1 -1 5 z 2 12 -1 5 z 17 -1 -1 5 22 49728 z 1 5 1 -1 2 5 1 -1 -1 1 5 z 1 5 -1 4 5 -1 2 5 z 1 5 1 -1 -1 1 5 1 -1 -1 3 5 z 1 5 -1 -1 3 5 -1 4 5 z 1 5 1 z 27 5 5 z 5 2 -1 -1 5 z 4 7 -1 5 z 3 12 -1 -1 5 z 2 17 -1 5 z 22 -1 -1 5 27 [/itex]

 Rule Form

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

 2007-05-02