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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(12/5), 6, 8/5, -z] == (1/9765625) (21 (-((625 (93 + 88 z))/(1 + z)^2) + (1/z^(3/5)) (10472 (Log[1 + z^(1/5)] + (-1)^(2/5) Log[1 - (-1)^(1/5) z^(1/5)] + (-1)^(4/5) Log[1 + (-1)^(2/5) z^(1/5)] - (-1)^(1/5) Log[1 - (-1)^(3/5) z^(1/5)] - (-1)^(3/5) Log[1 + (-1)^(4/5) z^(1/5)])) - 424116 (-(5/2) - z^(2/5) (Log[1 + z^(1/5)] + (-1)^(2/5) Log[1 - (-1)^(1/5) z^(1/5)] + (-1)^(4/5) Log[1 + (-1)^(2/5) z^(1/5)] - (-1)^(1/5) Log[1 - (-1)^(3/5) z^(1/5)] - (-1)^(3/5) Log[1 + (-1)^(4/5) z^(1/5)])) + 1938816 (-(5/7) + (5 z)/2 + z^(7/5) (Log[1 + z^(1/5)] + (-1)^(2/5) Log[1 - (-1)^(1/5) z^(1/5)] + (-1)^(4/5) Log[1 + (-1)^(2/5) z^(1/5)] - (-1)^(1/5) Log[1 - (-1)^(3/5) z^(1/5)] - (-1)^(3/5) Log[1 + (-1)^(4/5) z^(1/5)])) - 1992672 ((-(5/84)) (7 - 12 z + 42 z^2) - z^(12/5) (Log[1 + z^(1/5)] + (-1)^(2/5) Log[1 - (-1)^(1/5) z^(1/5)] + (-1)^(4/5) Log[1 + (-1)^(2/5) z^(1/5)] - (-1)^(1/5) Log[1 - (-1)^(3/5) z^(1/5)] - (-1)^(3/5) Log[1 + (-1)^(4/5) z^(1/5)]))))

 Standard Form

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 MathML Form

 2 F 1 ( - 12 5 , 6 ; 8 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["12", "5"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["6", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["8", "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 9765625 ( 21 ( - 625 ( 88 z + 93 ) ( z + 1 ) 2 + 1 z 3 / 5 ( 10472 ( log ( z 5 + 1 ) + ( - 1 ) 2 / 5 log ( 1 - - 1 5 z 5 ) + ( - 1 ) 4 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) - - 1 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) - ( - 1 ) 3 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) ) - 424116 ( - z 2 / 5 ( log ( z 5 + 1 ) + ( - 1 ) 2 / 5 log ( 1 - - 1 5 z 5 ) + ( - 1 ) 4 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) - - 1 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) - ( - 1 ) 3 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) - 5 2 ) + 1938816 ( ( log ( z 5 + 1 ) + ( - 1 ) 2 / 5 log ( 1 - - 1 5 z 5 ) + ( - 1 ) 4 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) - - 1 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) - ( - 1 ) 3 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) z 7 / 5 + 5 z 2 - 5 7 ) - 1992672 ( - ( log ( z 5 + 1 ) + ( - 1 ) 2 / 5 log ( 1 - - 1 5 z 5 ) + ( - 1 ) 4 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) - - 1 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) - ( - 1 ) 3 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) z 12 / 5 - 5 84 ( 42 z 2 - 12 z + 7 ) ) ) ) HypergeometricPFQ -1 12 5 6 8 5 -1 z 1 9765625 21 -1 625 88 z 93 z 1 2 -1 1 z 3 5 -1 10472 z 1 5 1 -1 2 5 1 -1 -1 1 5 z 1 5 -1 4 5 -1 2 5 z 1 5 1 -1 -1 1 5 1 -1 -1 3 5 z 1 5 -1 -1 3 5 -1 4 5 z 1 5 1 -1 424116 -1 z 2 5 z 1 5 1 -1 2 5 1 -1 -1 1 5 z 1 5 -1 4 5 -1 2 5 z 1 5 1 -1 -1 1 5 1 -1 -1 3 5 z 1 5 -1 -1 3 5 -1 4 5 z 1 5 1 -1 5 2 1938816 z 1 5 1 -1 2 5 1 -1 -1 1 5 z 1 5 -1 4 5 -1 2 5 z 1 5 1 -1 -1 1 5 1 -1 -1 3 5 z 1 5 -1 -1 3 5 -1 4 5 z 1 5 1 z 7 5 5 z 2 -1 -1 5 7 -1 1992672 -1 z 1 5 1 -1 2 5 1 -1 -1 1 5 z 1 5 -1 4 5 -1 2 5 z 1 5 1 -1 -1 1 5 1 -1 -1 3 5 z 1 5 -1 -1 3 5 -1 4 5 z 1 5 1 z 12 5 -1 5 84 42 z 2 -1 12 z 7 [/itex]

 Rule Form

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

 2007-05-02