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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[1/5, 1, 21/5, z] == -((1/(1875 z^(16/5))) (8 (-330 z^(1/5) + 935 z^(6/5) - 855 z^(11/5) + 66 (-1 + z)^3 Log[1 - z^(1/5)] + 66 (-1)^(4/5) (-1 + z)^3 Log[1 + (-1)^(1/5) z^(1/5)] + 66 (-1)^(3/5) Log[1 - (-1)^(2/5) z^(1/5)] - 198 (-1)^(3/5) z Log[1 - (-1)^(2/5) z^(1/5)] + 198 (-1)^(3/5) z^2 Log[1 - (-1)^(2/5) z^(1/5)] - 66 (-1)^(3/5) z^3 Log[1 - (-1)^(2/5) z^(1/5)] - 66 (-1)^(2/5) Log[1 + (-1)^(3/5) z^(1/5)] + 198 (-1)^(2/5) z Log[1 + (-1)^(3/5) z^(1/5)] - 198 (-1)^(2/5) z^2 Log[1 + (-1)^(3/5) z^(1/5)] + 66 (-1)^(2/5) z^3 Log[1 + (-1)^(3/5) z^(1/5)] + 66 (-1)^(1/5) Log[1 - (-1)^(4/5) z^(1/5)] - 198 (-1)^(1/5) z Log[1 - (-1)^(4/5) z^(1/5)] + 198 (-1)^(1/5) z^2 Log[1 - (-1)^(4/5) z^(1/5)] - 66 (-1)^(1/5) z^3 Log[1 - (-1)^(4/5) z^(1/5)])))

 Standard Form

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 MathML Form

 2 F 1 ( 1 5 , 1 ; 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["1", 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 1875 z 16 / 5 ( 8 ( 66 log ( 1 - z 5 ) ( z - 1 ) 3 + 66 ( - 1 ) 4 / 5 log ( - 1 5 z 5 + 1 ) ( z - 1 ) 3 - 855 z 11 / 5 + 935 z 6 / 5 - 66 ( - 1 ) 3 / 5 z 3 log ( 1 - ( - 1 ) 2 / 5 z 5 ) + 198 ( - 1 ) 3 / 5 z 2 log ( 1 - ( - 1 ) 2 / 5 z 5 ) - 198 ( - 1 ) 3 / 5 z log ( 1 - ( - 1 ) 2 / 5 z 5 ) + 66 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) + 66 ( - 1 ) 2 / 5 z 3 log ( ( - 1 ) 3 / 5 z 5 + 1 ) - 198 ( - 1 ) 2 / 5 z 2 log ( ( - 1 ) 3 / 5 z 5 + 1 ) + 198 ( - 1 ) 2 / 5 z log ( ( - 1 ) 3 / 5 z 5 + 1 ) - 66 ( - 1 ) 2 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) - 66 - 1 5 z 3 log ( 1 - ( - 1 ) 4 / 5 z 5 ) + 198 - 1 5 z 2 log ( 1 - ( - 1 ) 4 / 5 z 5 ) - 198 - 1 5 z log ( 1 - ( - 1 ) 4 / 5 z 5 ) + 66 - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) - 330 z 5 ) ) HypergeometricPFQ 1 5 1 21 5 z -1 1 1875 z 16 5 -1 8 66 1 -1 z 1 5 z -1 3 66 -1 4 5 -1 1 5 z 1 5 1 z -1 3 -1 855 z 11 5 935 z 6 5 -1 66 -1 3 5 z 3 1 -1 -1 2 5 z 1 5 198 -1 3 5 z 2 1 -1 -1 2 5 z 1 5 -1 198 -1 3 5 z 1 -1 -1 2 5 z 1 5 66 -1 3 5 1 -1 -1 2 5 z 1 5 66 -1 2 5 z 3 -1 3 5 z 1 5 1 -1 198 -1 2 5 z 2 -1 3 5 z 1 5 1 198 -1 2 5 z -1 3 5 z 1 5 1 -1 66 -1 2 5 -1 3 5 z 1 5 1 -1 66 -1 1 5 z 3 1 -1 -1 4 5 z 1 5 198 -1 1 5 z 2 1 -1 -1 4 5 z 1 5 -1 198 -1 1 5 z 1 -1 -1 4 5 z 1 5 66 -1 1 5 1 -1 -1 4 5 z 1 5 -1 330 z 1 5 [/itex]

 Rule Form

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

 2007-05-02