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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.auy7.01

 Input Form

 Hypergeometric2F1[-(8/5), 2, 2/5, z] == (1/125) (125 - 520 z - 24 z^(3/5) (-8 + 13 z) Log[1 - z^(1/5)] + 24 (-1)^(3/5) z^(3/5) (-8 + 13 z) Log[1 + (-1)^(1/5) z^(1/5)] - 192 (-1)^(1/5) z^(3/5) Log[1 - (-1)^(2/5) z^(1/5)] + 312 (-1)^(1/5) z^(8/5) Log[1 - (-1)^(2/5) z^(1/5)] + 192 (-1)^(4/5) z^(3/5) Log[1 + (-1)^(3/5) z^(1/5)] - 312 (-1)^(4/5) z^(8/5) Log[1 + (-1)^(3/5) z^(1/5)] + 192 (-1)^(2/5) z^(3/5) Log[1 - (-1)^(4/5) z^(1/5)] - 312 (-1)^(2/5) z^(8/5) Log[1 - (-1)^(4/5) z^(1/5)])

 Standard Form

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 MathML Form

 2 F 1 ( - 8 5 , 2 ; 2 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["2", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["2", "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 ( 312 - 1 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 8 / 5 - 312 ( - 1 ) 4 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 8 / 5 - 312 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 8 / 5 - 520 z - 24 ( 13 z - 8 ) log ( 1 - z 5 ) z 3 / 5 + 24 ( - 1 ) 3 / 5 ( 13 z - 8 ) log ( - 1 5 z 5 + 1 ) z 3 / 5 - 192 - 1 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 3 / 5 + 192 ( - 1 ) 4 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 3 / 5 + 192 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 3 / 5 + 125 ) HypergeometricPFQ -1 8 5 2 2 5 z 1 125 312 -1 1 5 1 -1 -1 2 5 z 1 5 z 8 5 -1 312 -1 4 5 -1 3 5 z 1 5 1 z 8 5 -1 312 -1 2 5 1 -1 -1 4 5 z 1 5 z 8 5 -1 520 z -1 24 13 z -8 1 -1 z 1 5 z 3 5 24 -1 3 5 13 z -8 -1 1 5 z 1 5 1 z 3 5 -1 192 -1 1 5 1 -1 -1 2 5 z 1 5 z 3 5 192 -1 4 5 -1 3 5 z 1 5 1 z 3 5 192 -1 2 5 1 -1 -1 4 5 z 1 5 z 3 5 125 [/itex]

 Rule Form

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

 2007-05-02