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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(6/5), 3, 19/5, z] == (1/(78125 z^(14/5))) (21 (-1)^(1/5) (12 (-1)^(4/5) (-1 + z)^2 (9 + 22 z + 44 z^2) Log[1 - z^(1/5)] + 12 (-1 + z)^2 (9 + 22 z + 44 z^2) Log[1 + (-1)^(1/5) z^(1/5)] + (-1)^(1/5) (-12 (-1 + z)^2 (9 + 22 z + 44 z^2) Log[1 - (-1)^(2/5) z^(1/5)] + (-1)^(1/5) (12 (-1 + z)^2 (9 + 22 z + 44 z^2) Log[1 + (-1)^(3/5) z^(1/5)] + (-1)^(1/5) (5 (-1)^(1/5) z^(4/5) (27 + 24 z - 704 z^2 + 528 z^3) - 12 (-1 + z)^2 (9 + 22 z + 44 z^2) Log[1 - (-1)^(4/5) z^(1/5)])))))

 Standard Form

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 MathML Form

 2 F 1 ( - 6 5 , 3 ; 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["6", "5"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["3", 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 78125 z 14 / 5 ( 21 - 1 5 ( 12 ( - 1 ) 4 / 5 ( 44 z 2 + 22 z + 9 ) log ( 1 - z 5 ) ( z - 1 ) 2 + 12 ( 44 z 2 + 22 z + 9 ) log ( - 1 5 z 5 + 1 ) ( z - 1 ) 2 + - 1 5 ( - 1 5 ( 12 ( 44 z 2 + 22 z + 9 ) log ( ( - 1 ) 3 / 5 z 5 + 1 ) ( z - 1 ) 2 + - 1 5 ( 5 - 1 5 z 4 / 5 ( 528 z 3 - 704 z 2 + 24 z + 27 ) - 12 ( z - 1 ) 2 ( 44 z 2 + 22 z + 9 ) log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) ) - 12 ( z - 1 ) 2 ( 44 z 2 + 22 z + 9 ) log ( 1 - ( - 1 ) 2 / 5 z 5 ) ) ) ) HypergeometricPFQ -1 6 5 3 19 5 z 1 78125 z 14 5 -1 21 -1 1 5 12 -1 4 5 44 z 2 22 z 9 1 -1 z 1 5 z -1 2 12 44 z 2 22 z 9 -1 1 5 z 1 5 1 z -1 2 -1 1 5 -1 1 5 12 44 z 2 22 z 9 -1 3 5 z 1 5 1 z -1 2 -1 1 5 5 -1 1 5 z 4 5 528 z 3 -1 704 z 2 24 z 27 -1 12 z -1 2 44 z 2 22 z 9 1 -1 -1 4 5 z 1 5 -1 12 z -1 2 44 z 2 22 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