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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[3/5, 2, 18/5, -z] == -((1/(625 z^(13/5))) (52 (-1)^(1/5) (40 (-1)^(4/5) z^(3/5) + 15 (-1)^(4/5) z^(8/5) + 6 (-1)^(4/5) (-4 - 3 z + z^2) Log[1 + z^(1/5)] - 6 (-1)^(1/5) (-4 - 3 z + z^2) Log[1 - (-1)^(1/5) z^(1/5)] + 24 (-1)^(3/5) Log[1 + (-1)^(2/5) z^(1/5)] + 18 (-1)^(3/5) z Log[1 + (-1)^(2/5) z^(1/5)] - 6 (-1)^(3/5) z^2 Log[1 + (-1)^(2/5) z^(1/5)] - 24 Log[1 - (-1)^(3/5) z^(1/5)] - 18 z Log[1 - (-1)^(3/5) z^(1/5)] + 6 z^2 Log[1 - (-1)^(3/5) z^(1/5)] - 24 (-1)^(2/5) Log[1 + (-1)^(4/5) z^(1/5)] - 18 (-1)^(2/5) z Log[1 + (-1)^(4/5) z^(1/5)] + 6 (-1)^(2/5) z^2 Log[1 + (-1)^(4/5) z^(1/5)])))

 Standard Form

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 MathML Form

 2 F 1 ( 3 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[FractionBox["3", "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[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] - 1 625 z 13 / 5 ( 52 - 1 5 ( - 6 ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 2 + 6 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 2 + 6 ( - 1 ) 2 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 2 + 15 ( - 1 ) 4 / 5 z 8 / 5 + 18 ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z - 18 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z - 18 ( - 1 ) 2 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z + 40 ( - 1 ) 4 / 5 z 3 / 5 + 6 ( - 1 ) 4 / 5 ( z 2 - 3 z - 4 ) log ( z 5 + 1 ) - 6 - 1 5 ( z 2 - 3 z - 4 ) log ( 1 - - 1 5 z 5 ) + 24 ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) - 24 log ( 1 - ( - 1 ) 3 / 5 z 5 ) - 24 ( - 1 ) 2 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) ) HypergeometricPFQ 3 5 2 18 5 -1 z -1 1 625 z 13 5 -1 52 -1 1 5 -6 -1 3 5 -1 2 5 z 1 5 1 z 2 6 1 -1 -1 3 5 z 1 5 z 2 6 -1 2 5 -1 4 5 z 1 5 1 z 2 15 -1 4 5 z 8 5 18 -1 3 5 -1 2 5 z 1 5 1 z -1 18 1 -1 -1 3 5 z 1 5 z -1 18 -1 2 5 -1 4 5 z 1 5 1 z 40 -1 4 5 z 3 5 6 -1 4 5 z 2 -1 3 z -4 z 1 5 1 -1 6 -1 1 5 z 2 -1 3 z -4 1 -1 -1 1 5 z 1 5 24 -1 3 5 -1 2 5 z 1 5 1 -1 24 1 -1 -1 3 5 z 1 5 -1 24 -1 2 5 -1 4 5 z 1 5 1 [/itex]

 Rule Form

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

 2007-05-02