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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(18/5), 1, 27/5, -z] == (1/(273437500 z^(22/5))) (11 (-1)^(1/5) (278460 (-1)^(4/5) z^(2/5) + 2148120 (-1)^(4/5) z^(7/5) + 7206810 (-1)^(4/5) z^(12/5) + 13704600 (-1)^(4/5) z^(17/5) - 8758400 (-1)^(4/5) z^(22/5) - 4683840 (-1)^(4/5) z^(27/5) - 1415505 (-1)^(4/5) z^(32/5) - 185640 (-1)^(4/5) z^(37/5) + 111384 (-1)^(4/5) (1 + z)^8 Log[1 + z^(1/5)] + 111384 (-1)^(2/5) (1 + z)^8 Log[1 - (-1)^(1/5) z^(1/5)] + 111384 Log[1 + (-1)^(2/5) z^(1/5)] + 891072 z Log[1 + (-1)^(2/5) z^(1/5)] + 3118752 z^2 Log[1 + (-1)^(2/5) z^(1/5)] + 6237504 z^3 Log[1 + (-1)^(2/5) z^(1/5)] + 7796880 z^4 Log[1 + (-1)^(2/5) z^(1/5)] + 6237504 z^5 Log[1 + (-1)^(2/5) z^(1/5)] + 3118752 z^6 Log[1 + (-1)^(2/5) z^(1/5)] + 891072 z^7 Log[1 + (-1)^(2/5) z^(1/5)] + 111384 z^8 Log[1 + (-1)^(2/5) z^(1/5)] - 111384 (-1)^(3/5) Log[1 - (-1)^(3/5) z^(1/5)] - 891072 (-1)^(3/5) z Log[1 - (-1)^(3/5) z^(1/5)] - 3118752 (-1)^(3/5) z^2 Log[1 - (-1)^(3/5) z^(1/5)] - 6237504 (-1)^(3/5) z^3 Log[1 - (-1)^(3/5) z^(1/5)] - 7796880 (-1)^(3/5) z^4 Log[1 - (-1)^(3/5) z^(1/5)] - 6237504 (-1)^(3/5) z^5 Log[1 - (-1)^(3/5) z^(1/5)] - 3118752 (-1)^(3/5) z^6 Log[1 - (-1)^(3/5) z^(1/5)] - 891072 (-1)^(3/5) z^7 Log[1 - (-1)^(3/5) z^(1/5)] - 111384 (-1)^(3/5) z^8 Log[1 - (-1)^(3/5) z^(1/5)] - 111384 (-1)^(1/5) Log[1 + (-1)^(4/5) z^(1/5)] - 891072 (-1)^(1/5) z Log[1 + (-1)^(4/5) z^(1/5)] - 3118752 (-1)^(1/5) z^2 Log[1 + (-1)^(4/5) z^(1/5)] - 6237504 (-1)^(1/5) z^3 Log[1 + (-1)^(4/5) z^(1/5)] - 7796880 (-1)^(1/5) z^4 Log[1 + (-1)^(4/5) z^(1/5)] - 6237504 (-1)^(1/5) z^5 Log[1 + (-1)^(4/5) z^(1/5)] - 3118752 (-1)^(1/5) z^6 Log[1 + (-1)^(4/5) z^(1/5)] - 891072 (-1)^(1/5) z^7 Log[1 + (-1)^(4/5) z^(1/5)] - 111384 (-1)^(1/5) z^8 Log[1 + (-1)^(4/5) z^(1/5)]))

 Standard Form

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 MathML Form

 2 F 1 ( - 18 5 , 1 ; 27 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["18", "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["27", "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 273437500 z 22 / 5 ( 11 - 1 5 ( 111384 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 8 - 111384 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 8 - 111384 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 8 - 185640 ( - 1 ) 4 / 5 z 37 / 5 + 891072 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 7 - 891072 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 7 - 891072 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 7 - 1415505 ( - 1 ) 4 / 5 z 32 / 5 + 3118752 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 6 - 3118752 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 6 - 3118752 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 6 - 4683840 ( - 1 ) 4 / 5 z 27 / 5 + 6237504 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 5 - 6237504 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 5 - 6237504 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 5 - 8758400 ( - 1 ) 4 / 5 z 22 / 5 + 7796880 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 4 - 7796880 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 4 - 7796880 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 4 + 13704600 ( - 1 ) 4 / 5 z 17 / 5 + 6237504 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 3 - 6237504 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 3 - 6237504 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 3 + 7206810 ( - 1 ) 4 / 5 z 12 / 5 + 3118752 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 2 - 3118752 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 2 - 3118752 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 2 + 2148120 ( - 1 ) 4 / 5 z 7 / 5 + 891072 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z - 891072 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z - 891072 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z + 278460 ( - 1 ) 4 / 5 z 2 / 5 + 111384 ( - 1 ) 4 / 5 ( z + 1 ) 8 log ( z 5 + 1 ) + 111384 ( - 1 ) 2 / 5 ( z + 1 ) 8 log ( 1 - - 1 5 z 5 ) + 111384 log ( ( - 1 ) 2 / 5 z 5 + 1 ) - 111384 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) - 111384 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) ) HypergeometricPFQ -1 18 5 1 27 5 -1 z 1 273437500 z 22 5 -1 11 -1 1 5 111384 -1 2 5 z 1 5 1 z 8 -1 111384 -1 3 5 1 -1 -1 3 5 z 1 5 z 8 -1 111384 -1 1 5 -1 4 5 z 1 5 1 z 8 -1 185640 -1 4 5 z 37 5 891072 -1 2 5 z 1 5 1 z 7 -1 891072 -1 3 5 1 -1 -1 3 5 z 1 5 z 7 -1 891072 -1 1 5 -1 4 5 z 1 5 1 z 7 -1 1415505 -1 4 5 z 32 5 3118752 -1 2 5 z 1 5 1 z 6 -1 3118752 -1 3 5 1 -1 -1 3 5 z 1 5 z 6 -1 3118752 -1 1 5 -1 4 5 z 1 5 1 z 6 -1 4683840 -1 4 5 z 27 5 6237504 -1 2 5 z 1 5 1 z 5 -1 6237504 -1 3 5 1 -1 -1 3 5 z 1 5 z 5 -1 6237504 -1 1 5 -1 4 5 z 1 5 1 z 5 -1 8758400 -1 4 5 z 22 5 7796880 -1 2 5 z 1 5 1 z 4 -1 7796880 -1 3 5 1 -1 -1 3 5 z 1 5 z 4 -1 7796880 -1 1 5 -1 4 5 z 1 5 1 z 4 13704600 -1 4 5 z 17 5 6237504 -1 2 5 z 1 5 1 z 3 -1 6237504 -1 3 5 1 -1 -1 3 5 z 1 5 z 3 -1 6237504 -1 1 5 -1 4 5 z 1 5 1 z 3 7206810 -1 4 5 z 12 5 3118752 -1 2 5 z 1 5 1 z 2 -1 3118752 -1 3 5 1 -1 -1 3 5 z 1 5 z 2 -1 3118752 -1 1 5 -1 4 5 z 1 5 1 z 2 2148120 -1 4 5 z 7 5 891072 -1 2 5 z 1 5 1 z -1 891072 -1 3 5 1 -1 -1 3 5 z 1 5 z -1 891072 -1 1 5 -1 4 5 z 1 5 1 z 278460 -1 4 5 z 2 5 111384 -1 4 5 z 1 8 z 1 5 1 111384 -1 2 5 z 1 8 1 -1 -1 1 5 z 1 5 111384 -1 2 5 z 1 5 1 -1 111384 -1 3 5 1 -1 -1 3 5 z 1 5 -1 111384 -1 1 5 -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