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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.ayb8.01

 Input Form

 Hypergeometric2F1[2/5, 6, 17/5, z] == (1/1953125) (7 (-((125 (869 - 1443 z + 624 z^2))/(-1 + z)^3) - (1/z^(2/5)) (64584 (Log[1 - z^(1/5)] - (-1)^(3/5) Log[1 + (-1)^(1/5) z^(1/5)] - (-1)^(1/5) Log[1 - (-1)^(2/5) z^(1/5)] + (-1)^(4/5) Log[1 + (-1)^(3/5) z^(1/5)] + (-1)^(2/5) Log[1 - (-1)^(4/5) z^(1/5)])) - (1/z^(7/5)) (5616 (5 z^(2/5) + 2 Log[1 - z^(1/5)] - 2 (-1)^(3/5) Log[1 + (-1)^(1/5) z^(1/5)] - 2 (-1)^(1/5) Log[1 - (-1)^(2/5) z^(1/5)] + 2 (-1)^(4/5) Log[1 + (-1)^(3/5) z^(1/5)] + 2 (-1)^(2/5) Log[1 - (-1)^(4/5) z^(1/5)])) - (1/z^(12/5)) (156 (35 z^(2/5) + 10 z^(7/5) + 14 Log[1 - z^(1/5)] - 14 (-1)^(3/5) Log[1 + (-1)^(1/5) z^(1/5)] - 14 (-1)^(1/5) Log[1 - (-1)^(2/5) z^(1/5)] + 14 (-1)^(4/5) Log[1 + (-1)^(3/5) z^(1/5)] + 14 (-1)^(2/5) Log[1 - (-1)^(4/5) z^(1/5)]))))

 Standard Form

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 MathML Form

 2 F 1 ( 2 5 , 6 ; 17 5 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["2", "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["17", "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 1953125 ( 7 ( - 125 ( 624 z 2 - 1443 z + 869 ) ( z - 1 ) 3 - 1 z 2 / 5 ( 64584 ( log ( 1 - z 5 ) - ( - 1 ) 3 / 5 log ( - 1 5 z 5 + 1 ) - - 1 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) + ( - 1 ) 4 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) + ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) ) - 1 z 7 / 5 ( 5616 ( 2 log ( 1 - z 5 ) - 2 ( - 1 ) 3 / 5 log ( - 1 5 z 5 + 1 ) - 2 - 1 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) + 2 ( - 1 ) 4 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) + 2 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) + 5 z 2 / 5 ) ) - 1 z 12 / 5 ( 156 ( 10 z 7 / 5 + 35 z 2 / 5 + 14 log ( 1 - z 5 ) - 14 ( - 1 ) 3 / 5 log ( - 1 5 z 5 + 1 ) - 14 - 1 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) + 14 ( - 1 ) 4 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) + 14 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) ) ) ) HypergeometricPFQ 2 5 6 17 5 z 1 1953125 7 -1 125 624 z 2 -1 1443 z 869 z -1 3 -1 -1 1 z 2 5 -1 64584 1 -1 z 1 5 -1 -1 3 5 -1 1 5 z 1 5 1 -1 -1 1 5 1 -1 -1 2 5 z 1 5 -1 4 5 -1 3 5 z 1 5 1 -1 2 5 1 -1 -1 4 5 z 1 5 -1 1 z 7 5 -1 5616 2 1 -1 z 1 5 -1 2 -1 3 5 -1 1 5 z 1 5 1 -1 2 -1 1 5 1 -1 -1 2 5 z 1 5 2 -1 4 5 -1 3 5 z 1 5 1 2 -1 2 5 1 -1 -1 4 5 z 1 5 5 z 2 5 -1 1 z 12 5 -1 156 10 z 7 5 35 z 2 5 14 1 -1 z 1 5 -1 14 -1 3 5 -1 1 5 z 1 5 1 -1 14 -1 1 5 1 -1 -1 2 5 z 1 5 14 -1 4 5 -1 3 5 z 1 5 1 14 -1 2 5 1 -1 -1 4 5 z 1 5 [/itex]

 Rule Form

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

 2007-05-02