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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(1/5), 5, 14/5, -z] == (1/156250) (3 (-((125 (38 + 33 z))/(1 + z)^2) - (1/z^(4/5)) (1056 (Log[1 + z^(1/5)] - (-1)^(1/5) Log[1 - (-1)^(1/5) z^(1/5)] + (-1)^(2/5) Log[1 + (-1)^(2/5) z^(1/5)] - (-1)^(3/5) Log[1 - (-1)^(3/5) z^(1/5)] + (-1)^(4/5) Log[1 + (-1)^(4/5) z^(1/5)])) + (1/z^(9/5)) (33 (5 z^(4/5) + 4 Log[1 + z^(1/5)] - 4 (-1)^(1/5) Log[1 - (-1)^(1/5) z^(1/5)] + 4 (-1)^(2/5) Log[1 + (-1)^(2/5) z^(1/5)] - 4 (-1)^(3/5) Log[1 - (-1)^(3/5) z^(1/5)] + 4 (-1)^(4/5) Log[1 + (-1)^(4/5) z^(1/5)])) - 11088 (-5 + z^(1/5) (Log[1 + z^(1/5)] - (-1)^(1/5) Log[1 - (-1)^(1/5) z^(1/5)] + (-1)^(2/5) Log[1 + (-1)^(2/5) z^(1/5)] - (-1)^(3/5) Log[1 - (-1)^(3/5) z^(1/5)] + (-1)^(4/5) Log[1 + (-1)^(4/5) z^(1/5)]))))

 Standard Form

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 MathML Form

 2 F 1 ( - 1 5 , 5 ; 14 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["1", "5"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["5", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["14", "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 156250 ( 3 ( - 125 ( 33 z + 38 ) ( z + 1 ) 2 - 1 z 4 / 5 ( 1056 ( log ( z 5 + 1 ) - - 1 5 log ( 1 - - 1 5 z 5 ) + ( - 1 ) 2 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) - ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) + ( - 1 ) 4 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) ) + 1 z 9 / 5 ( 33 ( 4 log ( z 5 + 1 ) - 4 - 1 5 log ( 1 - - 1 5 z 5 ) + 4 ( - 1 ) 2 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) - 4 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) + 4 ( - 1 ) 4 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) + 5 z 4 / 5 ) ) - 11088 ( z 5 ( log ( z 5 + 1 ) - - 1 5 log ( 1 - - 1 5 z 5 ) + ( - 1 ) 2 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) - ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) + ( - 1 ) 4 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) - 5 ) ) ) HypergeometricPFQ -1 1 5 5 14 5 -1 z 1 156250 3 -1 125 33 z 38 z 1 2 -1 -1 1 z 4 5 -1 1056 z 1 5 1 -1 -1 1 5 1 -1 -1 1 5 z 1 5 -1 2 5 -1 2 5 z 1 5 1 -1 -1 3 5 1 -1 -1 3 5 z 1 5 -1 4 5 -1 4 5 z 1 5 1 1 z 9 5 -1 33 4 z 1 5 1 -1 4 -1 1 5 1 -1 -1 1 5 z 1 5 4 -1 2 5 -1 2 5 z 1 5 1 -1 4 -1 3 5 1 -1 -1 3 5 z 1 5 4 -1 4 5 -1 4 5 z 1 5 1 5 z 4 5 -1 11088 z 1 5 z 1 5 1 -1 -1 1 5 1 -1 -1 1 5 z 1 5 -1 2 5 -1 2 5 z 1 5 1 -1 -1 3 5 1 -1 -1 3 5 z 1 5 -1 4 5 -1 4 5 z 1 5 1 -5 [/itex]

 Rule Form

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

 2007-05-02