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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(8/5), 1, 7/5, z] == (1/(125 z^(2/5))) (65 z^(2/5) - 40 z^(7/5) - 24 (-1 + z)^2 Log[1 - z^(1/5)] + 24 (-1)^(3/5) (-1 + z)^2 Log[1 + (-1)^(1/5) z^(1/5)] + 24 (-1)^(1/5) Log[1 - (-1)^(2/5) z^(1/5)] - 48 (-1)^(1/5) z Log[1 - (-1)^(2/5) z^(1/5)] + 24 (-1)^(1/5) z^2 Log[1 - (-1)^(2/5) z^(1/5)] - 24 (-1)^(4/5) Log[1 + (-1)^(3/5) z^(1/5)] + 48 (-1)^(4/5) z Log[1 + (-1)^(3/5) z^(1/5)] - 24 (-1)^(4/5) z^2 Log[1 + (-1)^(3/5) z^(1/5)] - 24 (-1)^(2/5) Log[1 - (-1)^(4/5) z^(1/5)] + 48 (-1)^(2/5) z Log[1 - (-1)^(4/5) z^(1/5)] - 24 (-1)^(2/5) z^2 Log[1 - (-1)^(4/5) z^(1/5)])

 Standard Form

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 MathML Form

 2 F 1 ( - 8 5 , 1 ; 7 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["8", "5"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["1", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["7", "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] 1 125 z 2 / 5 ( - 24 log ( 1 - z 5 ) ( z - 1 ) 2 + 24 ( - 1 ) 3 / 5 log ( - 1 5 z 5 + 1 ) ( z - 1 ) 2 - 40 z 7 / 5 + 24 - 1 5 z 2 log ( 1 - ( - 1 ) 2 / 5 z 5 ) - 48 - 1 5 z log ( 1 - ( - 1 ) 2 / 5 z 5 ) + 24 - 1 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) - 24 ( - 1 ) 4 / 5 z 2 log ( ( - 1 ) 3 / 5 z 5 + 1 ) + 48 ( - 1 ) 4 / 5 z log ( ( - 1 ) 3 / 5 z 5 + 1 ) - 24 ( - 1 ) 4 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) - 24 ( - 1 ) 2 / 5 z 2 log ( 1 - ( - 1 ) 4 / 5 z 5 ) + 48 ( - 1 ) 2 / 5 z log ( 1 - ( - 1 ) 4 / 5 z 5 ) - 24 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) + 65 z 2 / 5 ) HypergeometricPFQ -1 8 5 1 7 5 z 1 125 z 2 5 -1 -24 1 -1 z 1 5 z -1 2 24 -1 3 5 -1 1 5 z 1 5 1 z -1 2 -1 40 z 7 5 24 -1 1 5 z 2 1 -1 -1 2 5 z 1 5 -1 48 -1 1 5 z 1 -1 -1 2 5 z 1 5 24 -1 1 5 1 -1 -1 2 5 z 1 5 -1 24 -1 4 5 z 2 -1 3 5 z 1 5 1 48 -1 4 5 z -1 3 5 z 1 5 1 -1 24 -1 4 5 -1 3 5 z 1 5 1 -1 24 -1 2 5 z 2 1 -1 -1 4 5 z 1 5 48 -1 2 5 z 1 -1 -1 4 5 z 1 5 -1 24 -1 2 5 1 -1 -1 4 5 z 1 5 65 z 2 5 [/itex]

 Rule Form

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

 2007-05-02