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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.aub3.01

 Input Form

 Hypergeometric2F1[-(11/5), 5, 4/5, z] == (1/312500) (11 ((125 (-68 + 63 z))/(-1 + z)^2 - 11088 (-5 - z^(1/5) (Log[1 - z^(1/5)] - (-1)^(1/5) Log[1 + (-1)^(1/5) z^(1/5)] + (-1)^(2/5) Log[1 - (-1)^(2/5) z^(1/5)] - (-1)^(3/5) Log[1 + (-1)^(3/5) z^(1/5)] + (-1)^(4/5) Log[1 - (-1)^(4/5) z^(1/5)])) + 96096 (-(5/6) - 5 z - z^(6/5) (Log[1 - z^(1/5)] - (-1)^(1/5) Log[1 + (-1)^(1/5) z^(1/5)] + (-1)^(2/5) Log[1 - (-1)^(2/5) z^(1/5)] - (-1)^(3/5) Log[1 + (-1)^(3/5) z^(1/5)] + (-1)^(4/5) Log[1 - (-1)^(4/5) z^(1/5)])) - 135408 ((-(5/66)) (6 + 11 z + 66 z^2) - z^(11/5) (Log[1 - z^(1/5)] - (-1)^(1/5) Log[1 + (-1)^(1/5) z^(1/5)] + (-1)^(2/5) Log[1 - (-1)^(2/5) z^(1/5)] - (-1)^(3/5) Log[1 + (-1)^(3/5) z^(1/5)] + (-1)^(4/5) Log[1 - (-1)^(4/5) z^(1/5)]))))

 Standard Form

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 MathML Form

 2 F 1 ( - 11 5 , 5 ; 4 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["11", "5"]]], 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["4", "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] 1 312500 ( 11 ( 125 ( 63 z - 68 ) ( z - 1 ) 2 - 11088 ( - z 5 ( log ( 1 - z 5 ) - - 1 5 log ( - 1 5 z 5 + 1 ) + ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) - ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) + ( - 1 ) 4 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) - 5 ) + 96096 ( - ( log ( 1 - z 5 ) - - 1 5 log ( - 1 5 z 5 + 1 ) + ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) - ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) + ( - 1 ) 4 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) z 6 / 5 - 5 z - 5 6 ) - 135408 ( - ( log ( 1 - z 5 ) - - 1 5 log ( - 1 5 z 5 + 1 ) + ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) - ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) + ( - 1 ) 4 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) z 11 / 5 - 5 66 ( 66 z 2 + 11 z + 6 ) ) ) ) HypergeometricPFQ -1 11 5 5 4 5 z 1 312500 11 125 63 z -68 z -1 2 -1 -1 11088 -1 z 1 5 1 -1 z 1 5 -1 -1 1 5 -1 1 5 z 1 5 1 -1 2 5 1 -1 -1 2 5 z 1 5 -1 -1 3 5 -1 3 5 z 1 5 1 -1 4 5 1 -1 -1 4 5 z 1 5 -5 96096 -1 1 -1 z 1 5 -1 -1 1 5 -1 1 5 z 1 5 1 -1 2 5 1 -1 -1 2 5 z 1 5 -1 -1 3 5 -1 3 5 z 1 5 1 -1 4 5 1 -1 -1 4 5 z 1 5 z 6 5 -1 5 z -1 5 6 -1 135408 -1 1 -1 z 1 5 -1 -1 1 5 -1 1 5 z 1 5 1 -1 2 5 1 -1 -1 2 5 z 1 5 -1 -1 3 5 -1 3 5 z 1 5 1 -1 4 5 1 -1 -1 4 5 z 1 5 z 11 5 -1 5 66 66 z 2 11 z 6 [/itex]

 Rule Form

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

 2007-05-02