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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[4/5, 4, 29/5, -z] == (1/(390625 z^(24/5))) (798 (-1)^(1/5) (12 (-1)^(4/5) (-399 - 336 z + 36 z^2 - 16 z^3 + 11 z^4) Log[1 + z^(1/5)] + 12 (-399 - 336 z + 36 z^2 - 16 z^3 + 11 z^4) Log[1 - (-1)^(1/5) z^(1/5)] + (-1)^(1/5) (-12 (-399 - 336 z + 36 z^2 - 16 z^3 + 11 z^4) Log[1 + (-1)^(2/5) z^(1/5)] + (-1)^(1/5) (12 (-399 - 336 z + 36 z^2 - 16 z^3 + 11 z^4) Log[1 - (-1)^(3/5) z^(1/5)] - (-1)^(1/5) (5 (-1)^(1/5) z^(4/5) (1197 + 476 z - 214 z^2 + 132 z^3) + 12 (-399 - 336 z + 36 z^2 - 16 z^3 + 11 z^4) Log[1 + (-1)^(4/5) z^(1/5)])))))

 Standard Form

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 MathML Form

 2 F 1 ( 4 5 , 4 ; 29 5 ; - z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["4", "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[FractionBox["29", "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 390625 z 24 / 5 ( 798 - 1 5 ( 12 ( - 1 ) 4 / 5 ( 11 z 4 - 16 z 3 + 36 z 2 - 336 z - 399 ) log ( z 5 + 1 ) + 12 ( 11 z 4 - 16 z 3 + 36 z 2 - 336 z - 399 ) log ( 1 - - 1 5 z 5 ) + - 1 5 ( - 1 5 ( 12 ( 11 z 4 - 16 z 3 + 36 z 2 - 336 z - 399 ) log ( 1 - ( - 1 ) 3 / 5 z 5 ) - - 1 5 ( 5 - 1 5 z 4 / 5 ( 132 z 3 - 214 z 2 + 476 z + 1197 ) + 12 ( 11 z 4 - 16 z 3 + 36 z 2 - 336 z - 399 ) log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) ) - 12 ( 11 z 4 - 16 z 3 + 36 z 2 - 336 z - 399 ) log ( ( - 1 ) 2 / 5 z 5 + 1 ) ) ) ) HypergeometricPFQ 4 5 4 29 5 -1 z 1 390625 z 24 5 -1 798 -1 1 5 12 -1 4 5 11 z 4 -1 16 z 3 36 z 2 -1 336 z -399 z 1 5 1 12 11 z 4 -1 16 z 3 36 z 2 -1 336 z -399 1 -1 -1 1 5 z 1 5 -1 1 5 -1 1 5 12 11 z 4 -1 16 z 3 36 z 2 -1 336 z -399 1 -1 -1 3 5 z 1 5 -1 -1 1 5 5 -1 1 5 z 4 5 132 z 3 -1 214 z 2 476 z 1197 12 11 z 4 -1 16 z 3 36 z 2 -1 336 z -399 -1 4 5 z 1 5 1 -1 12 11 z 4 -1 16 z 3 36 z 2 -1 336 z -399 -1 2 5 z 1 5 1 [/itex]

 Rule Form

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

 2007-05-02