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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(19/5), 6, 1/5, z] == (1/9765625) (399 (-((625 (-121 + 116 z))/(-1 + z)^2) - 277704 (-(5/4) - z^(4/5) (Log[1 - z^(1/5)] + (-1)^(4/5) Log[1 + (-1)^(1/5) z^(1/5)] - (-1)^(3/5) Log[1 - (-1)^(2/5) z^(1/5)] + (-1)^(2/5) Log[1 + (-1)^(3/5) z^(1/5)] - (-1)^(1/5) Log[1 - (-1)^(4/5) z^(1/5)])) + 3147312 ((-(5/36)) (4 + 9 z) - z^(9/5) (Log[1 - z^(1/5)] + (-1)^(4/5) Log[1 + (-1)^(1/5) z^(1/5)] - (-1)^(3/5) Log[1 - (-1)^(2/5) z^(1/5)] + (-1)^(2/5) Log[1 + (-1)^(3/5) z^(1/5)] - (-1)^(1/5) Log[1 - (-1)^(4/5) z^(1/5)])) - 8767512 ((-(5/252)) (18 + 28 z + 63 z^2) - z^(14/5) (Log[1 - z^(1/5)] + (-1)^(4/5) Log[1 + (-1)^(1/5) z^(1/5)] - (-1)^(3/5) Log[1 - (-1)^(2/5) z^(1/5)] + (-1)^(2/5) Log[1 + (-1)^(3/5) z^(1/5)] - (-1)^(1/5) Log[1 - (-1)^(4/5) z^(1/5)])) + 6767904 (-(5/19) - (5 z)/14 - (5 z^2)/9 - (5 z^3)/4 - z^(19/5) (Log[1 - z^(1/5)] + (-1)^(4/5) Log[1 + (-1)^(1/5) z^(1/5)] - (-1)^(3/5) Log[1 - (-1)^(2/5) z^(1/5)] + (-1)^(2/5) Log[1 + (-1)^(3/5) z^(1/5)] - (-1)^(1/5) Log[1 - (-1)^(4/5) z^(1/5)]))))

 Standard Form

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 MathML Form

 2 F 1 ( - 19 5 , 6 ; 1 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["19", "5"]]], 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["1", "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 9765625 ( 399 ( - 625 ( 116 z - 121 ) ( z - 1 ) 2 - 277704 ( - z 4 / 5 ( log ( 1 - z 5 ) + ( - 1 ) 4 / 5 log ( - 1 5 z 5 + 1 ) - ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) + ( - 1 ) 2 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) - - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) - 5 4 ) + 3147312 ( - ( log ( 1 - z 5 ) + ( - 1 ) 4 / 5 log ( - 1 5 z 5 + 1 ) - ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) + ( - 1 ) 2 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) - - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) z 9 / 5 - 5 36 ( 9 z + 4 ) ) - 8767512 ( - ( log ( 1 - z 5 ) + ( - 1 ) 4 / 5 log ( - 1 5 z 5 + 1 ) - ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) + ( - 1 ) 2 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) - - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) z 14 / 5 - 5 252 ( 63 z 2 + 28 z + 18 ) ) + 6767904 ( - ( log ( 1 - z 5 ) + ( - 1 ) 4 / 5 log ( - 1 5 z 5 + 1 ) - ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) + ( - 1 ) 2 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) - - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) z 19 / 5 - 5 z 3 4 - 5 z 2 9 - 5 z 14 - 5 19 ) ) ) HypergeometricPFQ -1 19 5 6 1 5 z 1 9765625 399 -1 625 116 z -121 z -1 2 -1 -1 277704 -1 z 4 5 1 -1 z 1 5 -1 4 5 -1 1 5 z 1 5 1 -1 -1 3 5 1 -1 -1 2 5 z 1 5 -1 2 5 -1 3 5 z 1 5 1 -1 -1 1 5 1 -1 -1 4 5 z 1 5 -1 5 4 3147312 -1 1 -1 z 1 5 -1 4 5 -1 1 5 z 1 5 1 -1 -1 3 5 1 -1 -1 2 5 z 1 5 -1 2 5 -1 3 5 z 1 5 1 -1 -1 1 5 1 -1 -1 4 5 z 1 5 z 9 5 -1 5 36 9 z 4 -1 8767512 -1 1 -1 z 1 5 -1 4 5 -1 1 5 z 1 5 1 -1 -1 3 5 1 -1 -1 2 5 z 1 5 -1 2 5 -1 3 5 z 1 5 1 -1 -1 1 5 1 -1 -1 4 5 z 1 5 z 14 5 -1 5 252 63 z 2 28 z 18 6767904 -1 1 -1 z 1 5 -1 4 5 -1 1 5 z 1 5 1 -1 -1 3 5 1 -1 -1 2 5 z 1 5 -1 2 5 -1 3 5 z 1 5 1 -1 -1 1 5 1 -1 -1 4 5 z 1 5 z 19 5 -1 5 z 3 4 -1 -1 5 z 2 9 -1 -1 5 z 14 -1 -1 5 19 [/itex]

 Rule Form

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

 2007-05-02