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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[1/5, 3, 26/5, -z] == -((1/(78125 z^(21/5))) (154 (-1)^(1/5) (-2640 (-1)^(4/5) z^(1/5) - 3520 (-1)^(4/5) z^(6/5) - 120 (-1)^(4/5) z^(11/5) + 135 (-1)^(4/5) z^(16/5) + 12 (-1)^(4/5) (1 + z)^2 (44 - 22 z + 9 z^2) Log[1 + z^(1/5)] - 12 (-1)^(3/5) (1 + z)^2 (44 - 22 z + 9 z^2) Log[1 - (-1)^(1/5) z^(1/5)] + 528 (-1)^(2/5) Log[1 + (-1)^(2/5) z^(1/5)] + 792 (-1)^(2/5) z Log[1 + (-1)^(2/5) z^(1/5)] + 108 (-1)^(2/5) z^2 Log[1 + (-1)^(2/5) z^(1/5)] - 48 (-1)^(2/5) z^3 Log[1 + (-1)^(2/5) z^(1/5)] + 108 (-1)^(2/5) z^4 Log[1 + (-1)^(2/5) z^(1/5)] - 528 (-1)^(1/5) Log[1 - (-1)^(3/5) z^(1/5)] - 792 (-1)^(1/5) z Log[1 - (-1)^(3/5) z^(1/5)] - 108 (-1)^(1/5) z^2 Log[1 - (-1)^(3/5) z^(1/5)] + 48 (-1)^(1/5) z^3 Log[1 - (-1)^(3/5) z^(1/5)] - 108 (-1)^(1/5) z^4 Log[1 - (-1)^(3/5) z^(1/5)] + 528 Log[1 + (-1)^(4/5) z^(1/5)] + 792 z Log[1 + (-1)^(4/5) z^(1/5)] + 108 z^2 Log[1 + (-1)^(4/5) z^(1/5)] - 48 z^3 Log[1 + (-1)^(4/5) z^(1/5)] + 108 z^4 Log[1 + (-1)^(4/5) z^(1/5)])))

 Standard Form

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 MathML Form

 2 F 1 ( 1 5 , 3 ; 26 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["1", "5"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["3", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["26", "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 78125 z 21 / 5 ( 154 - 1 5 ( 108 ( - 1 ) 2 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 4 - 108 - 1 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 4 + 108 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 4 + 135 ( - 1 ) 4 / 5 z 16 / 5 - 48 ( - 1 ) 2 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 3 + 48 - 1 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 3 - 48 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 3 - 120 ( - 1 ) 4 / 5 z 11 / 5 + 108 ( - 1 ) 2 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 2 - 108 - 1 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 2 + 108 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 2 - 3520 ( - 1 ) 4 / 5 z 6 / 5 + 792 ( - 1 ) 2 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z - 792 - 1 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z + 792 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z - 2640 ( - 1 ) 4 / 5 z 5 + 12 ( - 1 ) 4 / 5 ( z + 1 ) 2 ( 9 z 2 - 22 z + 44 ) log ( z 5 + 1 ) - 12 ( - 1 ) 3 / 5 ( z + 1 ) 2 ( 9 z 2 - 22 z + 44 ) log ( 1 - - 1 5 z 5 ) + 528 ( - 1 ) 2 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) - 528 - 1 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) + 528 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) ) HypergeometricPFQ 1 5 3 26 5 -1 z -1 1 78125 z 21 5 -1 154 -1 1 5 108 -1 2 5 -1 2 5 z 1 5 1 z 4 -1 108 -1 1 5 1 -1 -1 3 5 z 1 5 z 4 108 -1 4 5 z 1 5 1 z 4 135 -1 4 5 z 16 5 -1 48 -1 2 5 -1 2 5 z 1 5 1 z 3 48 -1 1 5 1 -1 -1 3 5 z 1 5 z 3 -1 48 -1 4 5 z 1 5 1 z 3 -1 120 -1 4 5 z 11 5 108 -1 2 5 -1 2 5 z 1 5 1 z 2 -1 108 -1 1 5 1 -1 -1 3 5 z 1 5 z 2 108 -1 4 5 z 1 5 1 z 2 -1 3520 -1 4 5 z 6 5 792 -1 2 5 -1 2 5 z 1 5 1 z -1 792 -1 1 5 1 -1 -1 3 5 z 1 5 z 792 -1 4 5 z 1 5 1 z -1 2640 -1 4 5 z 1 5 12 -1 4 5 z 1 2 9 z 2 -1 22 z 44 z 1 5 1 -1 12 -1 3 5 z 1 2 9 z 2 -1 22 z 44 1 -1 -1 1 5 z 1 5 528 -1 2 5 -1 2 5 z 1 5 1 -1 528 -1 1 5 1 -1 -1 3 5 z 1 5 528 -1 4 5 z 1 5 1 [/itex]

 Rule Form

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

 2007-05-02