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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(22/5), 6, 3/5, z] == (1/48828125) (2618 (3125/(-1 + z) - 35343 (-(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)])) + 646272 ((-(5/14)) (2 + 7 z) - 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)])) - 2989008 ((-(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)])) + 4923072 (-(5/17) - (5 z)/12 - (5 z^2)/7 - (5 z^3)/2 - z^(17/5) (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)])) - 2629368 (-(5/22) - (5 z)/17 - (5 z^2)/12 - (5 z^3)/7 - (5 z^4)/2 - z^(22/5) (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 ( - 22 5 , 6 ; 3 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["22", "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["3", "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 48828125 ( 2618 ( - 35343 ( - z 2 / 5 ( log ( 1 - z 5 ) + ( - 1 ) 2 / 5 log ( - 1 5 z 5 + 1 ) + ( - 1 ) 4 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) - - 1 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) - ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) - 5 2 ) + 646272 ( - ( log ( 1 - z 5 ) + ( - 1 ) 2 / 5 log ( - 1 5 z 5 + 1 ) + ( - 1 ) 4 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) - - 1 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) - ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) z 7 / 5 - 5 14 ( 7 z + 2 ) ) - 2989008 ( - ( log ( 1 - z 5 ) + ( - 1 ) 2 / 5 log ( - 1 5 z 5 + 1 ) + ( - 1 ) 4 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) - - 1 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) - ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) z 12 / 5 - 5 84 ( 42 z 2 + 12 z + 7 ) ) + 4923072 ( - ( log ( 1 - z 5 ) + ( - 1 ) 2 / 5 log ( - 1 5 z 5 + 1 ) + ( - 1 ) 4 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) - - 1 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) - ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) z 17 / 5 - 5 z 3 2 - 5 z 2 7 - 5 z 12 - 5 17 ) - 2629368 ( - ( log ( 1 - z 5 ) + ( - 1 ) 2 / 5 log ( - 1 5 z 5 + 1 ) + ( - 1 ) 4 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) - - 1 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) - ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) z 22 / 5 - 5 z 4 2 - 5 z 3 7 - 5 z 2 12 - 5 z 17 - 5 22 ) + 3125 z - 1 ) ) HypergeometricPFQ -1 22 5 6 3 5 z 1 48828125 2618 -35343 -1 z 2 5 1 -1 z 1 5 -1 2 5 -1 1 5 z 1 5 1 -1 4 5 1 -1 -1 2 5 z 1 5 -1 -1 1 5 -1 3 5 z 1 5 1 -1 -1 3 5 1 -1 -1 4 5 z 1 5 -1 5 2 646272 -1 1 -1 z 1 5 -1 2 5 -1 1 5 z 1 5 1 -1 4 5 1 -1 -1 2 5 z 1 5 -1 -1 1 5 -1 3 5 z 1 5 1 -1 -1 3 5 1 -1 -1 4 5 z 1 5 z 7 5 -1 5 14 7 z 2 -1 2989008 -1 1 -1 z 1 5 -1 2 5 -1 1 5 z 1 5 1 -1 4 5 1 -1 -1 2 5 z 1 5 -1 -1 1 5 -1 3 5 z 1 5 1 -1 -1 3 5 1 -1 -1 4 5 z 1 5 z 12 5 -1 5 84 42 z 2 12 z 7 4923072 -1 1 -1 z 1 5 -1 2 5 -1 1 5 z 1 5 1 -1 4 5 1 -1 -1 2 5 z 1 5 -1 -1 1 5 -1 3 5 z 1 5 1 -1 -1 3 5 1 -1 -1 4 5 z 1 5 z 17 5 -1 5 z 3 2 -1 -1 5 z 2 7 -1 -1 5 z 12 -1 -1 5 17 -1 2629368 -1 1 -1 z 1 5 -1 2 5 -1 1 5 z 1 5 1 -1 4 5 1 -1 -1 2 5 z 1 5 -1 -1 1 5 -1 3 5 z 1 5 1 -1 -1 3 5 1 -1 -1 4 5 z 1 5 z 22 5 -1 5 z 4 2 -1 -1 5 z 3 7 -1 -1 5 z 2 12 -1 -1 5 z 17 -1 -1 5 22 3125 z -1 -1 [/itex]

 Rule Form

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

 2007-05-02