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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(2/5), 2, 18/5, z] == -((1/(9375 z^(13/5))) (52 (-1)^(1/5) (80 (-1)^(4/5) z^(3/5) - 60 (-1)^(4/5) z^(8/5) + 105 (-1)^(4/5) z^(13/5) + 6 (-1)^(4/5) (-1 + z)^2 (8 + 7 z) Log[1 - z^(1/5)] - 6 (-1)^(1/5) (-1 + z)^2 (8 + 7 z) Log[1 + (-1)^(1/5) z^(1/5)] - 48 (-1)^(3/5) Log[1 - (-1)^(2/5) z^(1/5)] + 54 (-1)^(3/5) z Log[1 - (-1)^(2/5) z^(1/5)] + 36 (-1)^(3/5) z^2 Log[1 - (-1)^(2/5) z^(1/5)] - 42 (-1)^(3/5) z^3 Log[1 - (-1)^(2/5) z^(1/5)] + 48 Log[1 + (-1)^(3/5) z^(1/5)] - 54 z Log[1 + (-1)^(3/5) z^(1/5)] - 36 z^2 Log[1 + (-1)^(3/5) z^(1/5)] + 42 z^3 Log[1 + (-1)^(3/5) z^(1/5)] + 48 (-1)^(2/5) Log[1 - (-1)^(4/5) z^(1/5)] - 54 (-1)^(2/5) z Log[1 - (-1)^(4/5) z^(1/5)] - 36 (-1)^(2/5) z^2 Log[1 - (-1)^(4/5) z^(1/5)] + 42 (-1)^(2/5) z^3 Log[1 - (-1)^(4/5) z^(1/5)])))

 Standard Form

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 MathML Form

 2 F 1 ( - 2 5 , 2 ; 18 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["2", "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["18", "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 9375 z 13 / 5 ( 52 - 1 5 ( - 42 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 3 + 42 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 3 + 42 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 3 + 105 ( - 1 ) 4 / 5 z 13 / 5 + 36 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 2 - 36 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 2 - 36 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 2 - 60 ( - 1 ) 4 / 5 z 8 / 5 + 54 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z - 54 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z - 54 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z + 80 ( - 1 ) 4 / 5 z 3 / 5 + 6 ( - 1 ) 4 / 5 ( z - 1 ) 2 ( 7 z + 8 ) log ( 1 - z 5 ) - 6 - 1 5 ( z - 1 ) 2 ( 7 z + 8 ) log ( - 1 5 z 5 + 1 ) - 48 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) + 48 log ( ( - 1 ) 3 / 5 z 5 + 1 ) + 48 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) ) HypergeometricPFQ -1 2 5 2 18 5 z -1 1 9375 z 13 5 -1 52 -1 1 5 -42 -1 3 5 1 -1 -1 2 5 z 1 5 z 3 42 -1 3 5 z 1 5 1 z 3 42 -1 2 5 1 -1 -1 4 5 z 1 5 z 3 105 -1 4 5 z 13 5 36 -1 3 5 1 -1 -1 2 5 z 1 5 z 2 -1 36 -1 3 5 z 1 5 1 z 2 -1 36 -1 2 5 1 -1 -1 4 5 z 1 5 z 2 -1 60 -1 4 5 z 8 5 54 -1 3 5 1 -1 -1 2 5 z 1 5 z -1 54 -1 3 5 z 1 5 1 z -1 54 -1 2 5 1 -1 -1 4 5 z 1 5 z 80 -1 4 5 z 3 5 6 -1 4 5 z -1 2 7 z 8 1 -1 z 1 5 -1 6 -1 1 5 z -1 2 7 z 8 -1 1 5 z 1 5 1 -1 48 -1 3 5 1 -1 -1 2 5 z 1 5 48 -1 3 5 z 1 5 1 48 -1 2 5 1 -1 -1 4 5 z 1 5 [/itex]

 Rule Form

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

 2007-05-02