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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[3/5, 2, 23/5, -z] == -((1/(3125 z^(18/5))) (39 (-1)^(1/5) (520 (-1)^(4/5) z^(3/5) + 765 (-1)^(4/5) z^(8/5) + 120 (-1)^(4/5) z^(13/5) + 24 (-1)^(4/5) (1 + z)^2 (-13 + 2 z) Log[1 + z^(1/5)] - 24 (-1)^(1/5) (1 + z)^2 (-13 + 2 z) Log[1 - (-1)^(1/5) z^(1/5)] + 312 (-1)^(3/5) Log[1 + (-1)^(2/5) z^(1/5)] + 576 (-1)^(3/5) z Log[1 + (-1)^(2/5) z^(1/5)] + 216 (-1)^(3/5) z^2 Log[1 + (-1)^(2/5) z^(1/5)] - 48 (-1)^(3/5) z^3 Log[1 + (-1)^(2/5) z^(1/5)] - 312 Log[1 - (-1)^(3/5) z^(1/5)] - 576 z Log[1 - (-1)^(3/5) z^(1/5)] - 216 z^2 Log[1 - (-1)^(3/5) z^(1/5)] + 48 z^3 Log[1 - (-1)^(3/5) z^(1/5)] - 312 (-1)^(2/5) Log[1 + (-1)^(4/5) z^(1/5)] - 576 (-1)^(2/5) z Log[1 + (-1)^(4/5) z^(1/5)] - 216 (-1)^(2/5) z^2 Log[1 + (-1)^(4/5) z^(1/5)] + 48 (-1)^(2/5) z^3 Log[1 + (-1)^(4/5) z^(1/5)])))

 Standard Form

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 MathML Form

 2 F 1 ( 3 5 , 2 ; 23 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["23", "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 3125 z 18 / 5 ( 39 - 1 5 ( - 48 ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 3 + 48 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 3 + 48 ( - 1 ) 2 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 3 + 120 ( - 1 ) 4 / 5 z 13 / 5 + 216 ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 2 - 216 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 2 - 216 ( - 1 ) 2 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 2 + 765 ( - 1 ) 4 / 5 z 8 / 5 + 576 ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z - 576 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z - 576 ( - 1 ) 2 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z + 520 ( - 1 ) 4 / 5 z 3 / 5 + 24 ( - 1 ) 4 / 5 ( z + 1 ) 2 ( 2 z - 13 ) log ( z 5 + 1 ) - 24 - 1 5 ( z + 1 ) 2 ( 2 z - 13 ) log ( 1 - - 1 5 z 5 ) + 312 ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) - 312 log ( 1 - ( - 1 ) 3 / 5 z 5 ) - 312 ( - 1 ) 2 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) ) HypergeometricPFQ 3 5 2 23 5 -1 z -1 1 3125 z 18 5 -1 39 -1 1 5 -48 -1 3 5 -1 2 5 z 1 5 1 z 3 48 1 -1 -1 3 5 z 1 5 z 3 48 -1 2 5 -1 4 5 z 1 5 1 z 3 120 -1 4 5 z 13 5 216 -1 3 5 -1 2 5 z 1 5 1 z 2 -1 216 1 -1 -1 3 5 z 1 5 z 2 -1 216 -1 2 5 -1 4 5 z 1 5 1 z 2 765 -1 4 5 z 8 5 576 -1 3 5 -1 2 5 z 1 5 1 z -1 576 1 -1 -1 3 5 z 1 5 z -1 576 -1 2 5 -1 4 5 z 1 5 1 z 520 -1 4 5 z 3 5 24 -1 4 5 z 1 2 2 z -13 z 1 5 1 -1 24 -1 1 5 z 1 2 2 z -13 1 -1 -1 1 5 z 1 5 312 -1 3 5 -1 2 5 z 1 5 1 -1 312 1 -1 -1 3 5 z 1 5 -1 312 -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