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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(21/5), 3, -(11/5), -z] == (168/625) (25/(1 + z) - 546 (5 (-(1/16) + z/11 - z^2/6 + z^3) - z^(16/5) (Log[1 + z^(1/5)] - (-1)^(1/5) Log[1 - (-1)^(1/5) z^(1/5)] + (-1)^(2/5) Log[1 + (-1)^(2/5) z^(1/5)] - (-1)^(3/5) Log[1 - (-1)^(3/5) z^(1/5)] + (-1)^(4/5) Log[1 + (-1)^(4/5) z^(1/5)])) + 806 (-(5/21) + (5 z)/16 - (5 z^2)/11 + (5 z^3)/6 - 5 z^4 + z^(21/5) (Log[1 + z^(1/5)] - (-1)^(1/5) Log[1 - (-1)^(1/5) z^(1/5)] + (-1)^(2/5) Log[1 + (-1)^(2/5) z^(1/5)] - (-1)^(3/5) Log[1 - (-1)^(3/5) z^(1/5)] + (-1)^(4/5) Log[1 + (-1)^(4/5) z^(1/5)])))

 Standard Form

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 MathML Form

 2 F 1 ( - 21 5 , 3 ; - 11 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["21", "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[RowBox[List["-", FractionBox["11", "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] 168 625 ( - 546 ( 5 ( z 3 - z 2 6 + z 11 - 1 16 ) - z 16 / 5 ( log ( z 5 + 1 ) - - 1 5 log ( 1 - - 1 5 z 5 ) + ( - 1 ) 2 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) - ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) + ( - 1 ) 4 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) ) + 806 ( ( log ( z 5 + 1 ) - - 1 5 log ( 1 - - 1 5 z 5 ) + ( - 1 ) 2 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) - ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) + ( - 1 ) 4 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) z 21 / 5 - 5 z 4 + 5 z 3 6 - 5 z 2 11 + 5 z 16 - 5 21 ) + 25 z + 1 ) HypergeometricPFQ -1 21 5 3 -1 11 5 -1 z 168 625 -546 5 z 3 -1 z 2 6 -1 z 11 -1 -1 1 16 -1 z 16 5 z 1 5 1 -1 -1 1 5 1 -1 -1 1 5 z 1 5 -1 2 5 -1 2 5 z 1 5 1 -1 -1 3 5 1 -1 -1 3 5 z 1 5 -1 4 5 -1 4 5 z 1 5 1 806 z 1 5 1 -1 -1 1 5 1 -1 -1 1 5 z 1 5 -1 2 5 -1 2 5 z 1 5 1 -1 -1 3 5 1 -1 -1 3 5 z 1 5 -1 4 5 -1 4 5 z 1 5 1 z 21 5 -1 5 z 4 5 z 3 6 -1 -1 5 z 2 11 -1 5 z 16 -1 -1 5 21 25 z 1 -1 [/itex]

 Rule Form

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

 2007-05-02