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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[1/5, 3, 21/5, z] == (1/(15625 z^(16/5))) (88 (-1)^(1/5) (-330 (-1)^(4/5) z^(1/5) + 35 (-1)^(4/5) z^(6/5) + 45 (-1)^(4/5) z^(11/5) + 6 (-1)^(4/5) (-11 + 3 z + 2 z^2 + 6 z^3) Log[1 - z^(1/5)] - 6 (-1)^(3/5) (-11 + 3 z + 2 z^2 + 6 z^3) Log[1 + (-1)^(1/5) z^(1/5)] - 66 (-1)^(2/5) Log[1 - (-1)^(2/5) z^(1/5)] + 18 (-1)^(2/5) z Log[1 - (-1)^(2/5) z^(1/5)] + 12 (-1)^(2/5) z^2 Log[1 - (-1)^(2/5) z^(1/5)] + 36 (-1)^(2/5) z^3 Log[1 - (-1)^(2/5) z^(1/5)] + 66 (-1)^(1/5) Log[1 + (-1)^(3/5) z^(1/5)] - 18 (-1)^(1/5) z Log[1 + (-1)^(3/5) z^(1/5)] - 12 (-1)^(1/5) z^2 Log[1 + (-1)^(3/5) z^(1/5)] - 36 (-1)^(1/5) z^3 Log[1 + (-1)^(3/5) z^(1/5)] - 66 Log[1 - (-1)^(4/5) z^(1/5)] + 18 z Log[1 - (-1)^(4/5) z^(1/5)] + 12 z^2 Log[1 - (-1)^(4/5) z^(1/5)] + 36 z^3 Log[1 - (-1)^(4/5) z^(1/5)]))

 Standard Form

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 MathML Form

 2 F 1 ( 1 5 , 3 ; 21 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["21", "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 15625 z 16 / 5 ( 88 - 1 5 ( 36 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 3 - 36 - 1 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 3 + 36 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 3 + 45 ( - 1 ) 4 / 5 z 11 / 5 + 12 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 2 - 12 - 1 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 2 + 12 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 2 + 35 ( - 1 ) 4 / 5 z 6 / 5 + 18 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z - 18 - 1 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z + 18 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z - 330 ( - 1 ) 4 / 5 z 5 + 6 ( - 1 ) 4 / 5 ( 6 z 3 + 2 z 2 + 3 z - 11 ) log ( 1 - z 5 ) - 6 ( - 1 ) 3 / 5 ( 6 z 3 + 2 z 2 + 3 z - 11 ) log ( - 1 5 z 5 + 1 ) - 66 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) + 66 - 1 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) - 66 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) ) HypergeometricPFQ 1 5 3 21 5 z 1 15625 z 16 5 -1 88 -1 1 5 36 -1 2 5 1 -1 -1 2 5 z 1 5 z 3 -1 36 -1 1 5 -1 3 5 z 1 5 1 z 3 36 1 -1 -1 4 5 z 1 5 z 3 45 -1 4 5 z 11 5 12 -1 2 5 1 -1 -1 2 5 z 1 5 z 2 -1 12 -1 1 5 -1 3 5 z 1 5 1 z 2 12 1 -1 -1 4 5 z 1 5 z 2 35 -1 4 5 z 6 5 18 -1 2 5 1 -1 -1 2 5 z 1 5 z -1 18 -1 1 5 -1 3 5 z 1 5 1 z 18 1 -1 -1 4 5 z 1 5 z -1 330 -1 4 5 z 1 5 6 -1 4 5 6 z 3 2 z 2 3 z -11 1 -1 z 1 5 -1 6 -1 3 5 6 z 3 2 z 2 3 z -11 -1 1 5 z 1 5 1 -1 66 -1 2 5 1 -1 -1 2 5 z 1 5 66 -1 1 5 -1 3 5 z 1 5 1 -1 66 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