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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.az0m.01

 Input Form

 Hypergeometric2F1[4/5, 6, 19/5, z] == (1/(1953125 (-1 + z)^3 z^(14/5))) (21 (-1)^(1/5) (132 (-1)^(4/5) (-1 + z)^3 (9 + 32 z + 84 z^2) Log[1 - z^(1/5)] + 132 (-1 + z)^3 (9 + 32 z + 84 z^2) Log[1 + (-1)^(1/5) z^(1/5)] + (-1)^(1/5) (-132 (-1 + z)^3 (9 + 32 z + 84 z^2) Log[1 - (-1)^(2/5) z^(1/5)] + (-1)^(1/5) (132 (-1 + z)^3 (9 + 32 z + 84 z^2) Log[1 + (-1)^(3/5) z^(1/5)] + (-1)^(1/5) (5 (-1)^(1/5) z^(4/5) (-297 - 297 z + 17948 z^2 - 27192 z^3 + 11088 z^4) - 132 (-1 + z)^3 (9 + 32 z + 84 z^2) Log[1 - (-1)^(4/5) z^(1/5)])))))

 Standard Form

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 MathML Form

 2 F 1 ( 4 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[FractionBox["4", "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["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 1953125 ( z - 1 ) 3 z 14 / 5 ( 21 - 1 5 ( 132 ( - 1 ) 4 / 5 ( 84 z 2 + 32 z + 9 ) log ( 1 - z 5 ) ( z - 1 ) 3 + 132 ( 84 z 2 + 32 z + 9 ) log ( - 1 5 z 5 + 1 ) ( z - 1 ) 3 + - 1 5 ( - 1 5 ( 132 ( 84 z 2 + 32 z + 9 ) log ( ( - 1 ) 3 / 5 z 5 + 1 ) ( z - 1 ) 3 + - 1 5 ( 5 - 1 5 z 4 / 5 ( 11088 z 4 - 27192 z 3 + 17948 z 2 - 297 z - 297 ) - 132 ( z - 1 ) 3 ( 84 z 2 + 32 z + 9 ) log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) ) - 132 ( z - 1 ) 3 ( 84 z 2 + 32 z + 9 ) log ( 1 - ( - 1 ) 2 / 5 z 5 ) ) ) ) HypergeometricPFQ 4 5 6 19 5 z 1 1953125 z -1 3 z 14 5 -1 21 -1 1 5 132 -1 4 5 84 z 2 32 z 9 1 -1 z 1 5 z -1 3 132 84 z 2 32 z 9 -1 1 5 z 1 5 1 z -1 3 -1 1 5 -1 1 5 132 84 z 2 32 z 9 -1 3 5 z 1 5 1 z -1 3 -1 1 5 5 -1 1 5 z 4 5 11088 z 4 -1 27192 z 3 17948 z 2 -1 297 z -297 -1 132 z -1 3 84 z 2 32 z 9 1 -1 -1 4 5 z 1 5 -1 132 z -1 3 84 z 2 32 z 9 1 -1 -1 2 5 z 1 5 [/itex]

 Rule Form

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

 2007-05-02