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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(9/5), 6, 11/5, -z] == (1/9765625) (9 ((625 (81 + 76 z))/(1 + z)^2 + (1/z^(1/5)) (114912 (Log[1 + z^(1/5)] + (-1)^(4/5) Log[1 - (-1)^(1/5) z^(1/5)] - (-1)^(3/5) Log[1 + (-1)^(2/5) z^(1/5)] + (-1)^(2/5) Log[1 - (-1)^(3/5) z^(1/5)] - (-1)^(1/5) Log[1 + (-1)^(4/5) z^(1/5)])) + (1/z^(6/5)) (1596 (5 z^(1/5) - Log[1 + z^(1/5)] - (-1)^(4/5) Log[1 - (-1)^(1/5) z^(1/5)] + (-1)^(3/5) Log[1 + (-1)^(2/5) z^(1/5)] - (-1)^(2/5) Log[1 - (-1)^(3/5) z^(1/5)] + (-1)^(1/5) Log[1 + (-1)^(4/5) z^(1/5)])) - 833112 (-(5/4) - z^(4/5) (Log[1 + z^(1/5)] + (-1)^(4/5) Log[1 - (-1)^(1/5) z^(1/5)] - (-1)^(3/5) Log[1 + (-1)^(2/5) z^(1/5)] + (-1)^(2/5) Log[1 - (-1)^(3/5) z^(1/5)] - (-1)^(1/5) Log[1 + (-1)^(4/5) z^(1/5)])) + 1049104 (-(5/9) + (5 z)/4 + z^(9/5) (Log[1 + z^(1/5)] + (-1)^(4/5) Log[1 - (-1)^(1/5) z^(1/5)] - (-1)^(3/5) Log[1 + (-1)^(2/5) z^(1/5)] + (-1)^(2/5) Log[1 - (-1)^(3/5) z^(1/5)] - (-1)^(1/5) Log[1 + (-1)^(4/5) z^(1/5)]))))

 Standard Form

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 MathML Form

 2 F 1 ( - 9 5 , 6 ; 11 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["9", "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["11", "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 ( 9 ( 625 ( 76 z + 81 ) ( z + 1 ) 2 + 1 z 5 ( 114912 ( log ( z 5 + 1 ) + ( - 1 ) 4 / 5 log ( 1 - - 1 5 z 5 ) - ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) + ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) - - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) ) + 1 z 6 / 5 ( 1596 ( - log ( z 5 + 1 ) - ( - 1 ) 4 / 5 log ( 1 - - 1 5 z 5 ) + ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) - ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) + - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) + 5 z 5 ) ) - 833112 ( - z 4 / 5 ( log ( z 5 + 1 ) + ( - 1 ) 4 / 5 log ( 1 - - 1 5 z 5 ) - ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) + ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) - - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) - 5 4 ) + 1049104 ( ( log ( z 5 + 1 ) + ( - 1 ) 4 / 5 log ( 1 - - 1 5 z 5 ) - ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) + ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) - - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) z 9 / 5 + 5 z 4 - 5 9 ) ) ) HypergeometricPFQ -1 9 5 6 11 5 -1 z 1 9765625 9 625 76 z 81 z 1 2 -1 1 z 1 5 -1 114912 z 1 5 1 -1 4 5 1 -1 -1 1 5 z 1 5 -1 -1 3 5 -1 2 5 z 1 5 1 -1 2 5 1 -1 -1 3 5 z 1 5 -1 -1 1 5 -1 4 5 z 1 5 1 1 z 6 5 -1 1596 -1 z 1 5 1 -1 -1 4 5 1 -1 -1 1 5 z 1 5 -1 3 5 -1 2 5 z 1 5 1 -1 -1 2 5 1 -1 -1 3 5 z 1 5 -1 1 5 -1 4 5 z 1 5 1 5 z 1 5 -1 833112 -1 z 4 5 z 1 5 1 -1 4 5 1 -1 -1 1 5 z 1 5 -1 -1 3 5 -1 2 5 z 1 5 1 -1 2 5 1 -1 -1 3 5 z 1 5 -1 -1 1 5 -1 4 5 z 1 5 1 -1 5 4 1049104 z 1 5 1 -1 4 5 1 -1 -1 1 5 z 1 5 -1 -1 3 5 -1 2 5 z 1 5 1 -1 2 5 1 -1 -1 3 5 z 1 5 -1 -1 1 5 -1 4 5 z 1 5 1 z 9 5 5 z 4 -1 -1 5 9 [/itex]

 Rule Form

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

 2007-05-02