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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(1/5), 6, 19/5, -z] == (1/(9765625 z^(14/5) (1 + z)^2)) (21 (-1)^(1/5) (132 (-1)^(4/5) (1 + z)^2 (3 - 16 z + 84 z^2 + 728 z^3) Log[1 + z^(1/5)] + 132 (1 + z)^2 (3 - 16 z + 84 z^2 + 728 z^3) Log[1 - (-1)^(1/5) z^(1/5)] - (-1)^(1/5) (132 (1 + z)^2 (3 - 16 z + 84 z^2 + 728 z^3) Log[1 + (-1)^(2/5) z^(1/5)] + (-1)^(1/5) (-132 (1 + z)^2 (3 - 16 z + 84 z^2 + 728 z^3) Log[1 - (-1)^(3/5) z^(1/5)] + (-1)^(1/5) (5 (-1)^(1/5) z^(4/5) (-99 + 374 z + 91016 z^2 + 187264 z^3 + 96096 z^4) + 132 (1 + z)^2 (3 - 16 z + 84 z^2 + 728 z^3) Log[1 + (-1)^(4/5) z^(1/5)])))))

 Standard Form

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 MathML Form

 2 F 1 ( - 1 5 , 6 ; 19 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["1", "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["19", "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 9765625 z 14 / 5 ( z + 1 ) 2 ( 21 - 1 5 ( 132 ( - 1 ) 4 / 5 ( 728 z 3 + 84 z 2 - 16 z + 3 ) log ( z 5 + 1 ) ( z + 1 ) 2 + 132 ( 728 z 3 + 84 z 2 - 16 z + 3 ) log ( 1 - - 1 5 z 5 ) ( z + 1 ) 2 - - 1 5 ( 132 ( 728 z 3 + 84 z 2 - 16 z + 3 ) log ( ( - 1 ) 2 / 5 z 5 + 1 ) ( z + 1 ) 2 + - 1 5 ( - 1 5 ( 132 ( 728 z 3 + 84 z 2 - 16 z + 3 ) log ( ( - 1 ) 4 / 5 z 5 + 1 ) ( z + 1 ) 2 + 5 - 1 5 z 4 / 5 ( 96096 z 4 + 187264 z 3 + 91016 z 2 + 374 z - 99 ) ) - 132 ( z + 1 ) 2 ( 728 z 3 + 84 z 2 - 16 z + 3 ) log ( 1 - ( - 1 ) 3 / 5 z 5 ) ) ) ) ) HypergeometricPFQ -1 1 5 6 19 5 -1 z 1 9765625 z 14 5 z 1 2 -1 21 -1 1 5 132 -1 4 5 728 z 3 84 z 2 -1 16 z 3 z 1 5 1 z 1 2 132 728 z 3 84 z 2 -1 16 z 3 1 -1 -1 1 5 z 1 5 z 1 2 -1 -1 1 5 132 728 z 3 84 z 2 -1 16 z 3 -1 2 5 z 1 5 1 z 1 2 -1 1 5 -1 1 5 132 728 z 3 84 z 2 -1 16 z 3 -1 4 5 z 1 5 1 z 1 2 5 -1 1 5 z 4 5 96096 z 4 187264 z 3 91016 z 2 374 z -99 -1 132 z 1 2 728 z 3 84 z 2 -1 16 z 3 1 -1 -1 3 5 z 1 5 [/itex]

 Rule Form

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

 2007-05-02