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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.asn3.01

 Input Form

 Hypergeometric2F1[-(16/5), 5, -(1/5), z] == (1/78125) (44 ((125 (-83 + 78 z))/(-1 + z)^2 - 48048 (-(5/6) - 5 z - z^(6/5) (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)])) + 270816 ((-(5/66)) (6 + 11 z + 66 z^2) - z^(11/5) (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)])) - 304668 ((-(5/528)) (33 + 48 z + 88 z^2 + 528 z^3) - z^(16/5) (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 ( - 16 5 , 5 ; - 1 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["16", "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[RowBox[List["-", FractionBox["1", "5"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["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 78125 ( 44 ( 125 ( 78 z - 83 ) ( z - 1 ) 2 - 48048 ( - ( log ( 1 - z 5 ) - - 1 5 log ( - 1 5 z 5 + 1 ) + ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) - ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) + ( - 1 ) 4 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) z 6 / 5 - 5 z - 5 6 ) + 270816 ( - ( log ( 1 - z 5 ) - - 1 5 log ( - 1 5 z 5 + 1 ) + ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) - ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) + ( - 1 ) 4 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) z 11 / 5 - 5 66 ( 66 z 2 + 11 z + 6 ) ) - 304668 ( - ( log ( 1 - z 5 ) - - 1 5 log ( - 1 5 z 5 + 1 ) + ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) - ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) + ( - 1 ) 4 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) z 16 / 5 - 5 528 ( 528 z 3 + 88 z 2 + 48 z + 33 ) ) ) ) HypergeometricPFQ -1 16 5 5 -1 1 5 z 1 78125 44 125 78 z -83 z -1 2 -1 -1 48048 -1 1 -1 z 1 5 -1 -1 1 5 -1 1 5 z 1 5 1 -1 2 5 1 -1 -1 2 5 z 1 5 -1 -1 3 5 -1 3 5 z 1 5 1 -1 4 5 1 -1 -1 4 5 z 1 5 z 6 5 -1 5 z -1 5 6 270816 -1 1 -1 z 1 5 -1 -1 1 5 -1 1 5 z 1 5 1 -1 2 5 1 -1 -1 2 5 z 1 5 -1 -1 3 5 -1 3 5 z 1 5 1 -1 4 5 1 -1 -1 4 5 z 1 5 z 11 5 -1 5 66 66 z 2 11 z 6 -1 304668 -1 1 -1 z 1 5 -1 -1 1 5 -1 1 5 z 1 5 1 -1 2 5 1 -1 -1 2 5 z 1 5 -1 -1 3 5 -1 3 5 z 1 5 1 -1 4 5 1 -1 -1 4 5 z 1 5 z 16 5 -1 5 528 528 z 3 88 z 2 48 z 33 [/itex]

 Rule Form

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

 2007-05-02