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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.arw0.01

 Input Form

 Hypergeometric2F1[-(18/5), 6, 22/5, -z] == (1/(30517578125 z^(17/5))) (17 (-1)^(1/5) (-393120 (-1)^(4/5) z^(2/5) + 3093480 (-1)^(4/5) z^(7/5) - 23914800 (-1)^(4/5) z^(12/5) - 1347252025 (-1)^(4/5) z^(17/5) - 4828720050 (-1)^(4/5) z^(22/5) - 5767606845 (-1)^(4/5) z^(27/5) - 2257174920 (-1)^(4/5) z^(32/5) + 6552 (-1)^(4/5) (1 + z)^2 (-24 + 230 z - 1840 z^2 + 30360 z^3 + 192280 z^4 + 206701 z^5) Log[1 + z^(1/5)] + 6552 (-1)^(2/5) (1 + z)^2 (-24 + 230 z - 1840 z^2 + 30360 z^3 + 192280 z^4 + 206701 z^5) Log[1 - (-1)^(1/5) z^(1/5)] - 157248 Log[1 + (-1)^(2/5) z^(1/5)] + 1192464 z Log[1 + (-1)^(2/5) z^(1/5)] - 9199008 z^2 Log[1 + (-1)^(2/5) z^(1/5)] + 176314320 z^3 Log[1 + (-1)^(2/5) z^(1/5)] + 1645600320 z^4 Log[1 + (-1)^(2/5) z^(1/5)] + 4072860792 z^5 Log[1 + (-1)^(2/5) z^(1/5)] + 3968428464 z^6 Log[1 + (-1)^(2/5) z^(1/5)] + 1354304952 z^7 Log[1 + (-1)^(2/5) z^(1/5)] + 157248 (-1)^(3/5) Log[1 - (-1)^(3/5) z^(1/5)] - 1192464 (-1)^(3/5) z Log[1 - (-1)^(3/5) z^(1/5)] + 9199008 (-1)^(3/5) z^2 Log[1 - (-1)^(3/5) z^(1/5)] - 176314320 (-1)^(3/5) z^3 Log[1 - (-1)^(3/5) z^(1/5)] - 1645600320 (-1)^(3/5) z^4 Log[1 - (-1)^(3/5) z^(1/5)] - 4072860792 (-1)^(3/5) z^5 Log[1 - (-1)^(3/5) z^(1/5)] - 3968428464 (-1)^(3/5) z^6 Log[1 - (-1)^(3/5) z^(1/5)] - 1354304952 (-1)^(3/5) z^7 Log[1 - (-1)^(3/5) z^(1/5)] + 157248 (-1)^(1/5) Log[1 + (-1)^(4/5) z^(1/5)] - 1192464 (-1)^(1/5) z Log[1 + (-1)^(4/5) z^(1/5)] + 9199008 (-1)^(1/5) z^2 Log[1 + (-1)^(4/5) z^(1/5)] - 176314320 (-1)^(1/5) z^3 Log[1 + (-1)^(4/5) z^(1/5)] - 1645600320 (-1)^(1/5) z^4 Log[1 + (-1)^(4/5) z^(1/5)] - 4072860792 (-1)^(1/5) z^5 Log[1 + (-1)^(4/5) z^(1/5)] - 3968428464 (-1)^(1/5) z^6 Log[1 + (-1)^(4/5) z^(1/5)] - 1354304952 (-1)^(1/5) z^7 Log[1 + (-1)^(4/5) z^(1/5)]))

 Standard Form

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 MathML Form

 2 F 1 ( - 18 5 , 6 ; 22 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["6", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["22", "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 30517578125 z 17 / 5 ( 17 - 1 5 ( 1354304952 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 7 - 1354304952 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 7 - 1354304952 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 7 - 2257174920 ( - 1 ) 4 / 5 z 32 / 5 + 3968428464 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 6 - 3968428464 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 6 - 3968428464 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 6 - 5767606845 ( - 1 ) 4 / 5 z 27 / 5 + 4072860792 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 5 - 4072860792 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 5 - 4072860792 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 5 - 4828720050 ( - 1 ) 4 / 5 z 22 / 5 + 1645600320 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 4 - 1645600320 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 4 - 1645600320 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 4 - 1347252025 ( - 1 ) 4 / 5 z 17 / 5 + 176314320 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 3 - 176314320 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 3 - 176314320 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 3 - 23914800 ( - 1 ) 4 / 5 z 12 / 5 - 9199008 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 2 + 9199008 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 2 + 9199008 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 2 + 3093480 ( - 1 ) 4 / 5 z 7 / 5 + 1192464 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z - 1192464 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z - 1192464 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z - 393120 ( - 1 ) 4 / 5 z 2 / 5 + 6552 ( - 1 ) 4 / 5 ( z + 1 ) 2 ( 206701 z 5 + 192280 z 4 + 30360 z 3 - 1840 z 2 + 230 z - 24 ) log ( z 5 + 1 ) + 6552 ( - 1 ) 2 / 5 ( z + 1 ) 2 ( 206701 z 5 + 192280 z 4 + 30360 z 3 - 1840 z 2 + 230 z - 24 ) log ( 1 - - 1 5 z 5 ) - 157248 log ( ( - 1 ) 2 / 5 z 5 + 1 ) + 157248 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) + 157248 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) ) HypergeometricPFQ -1 18 5 6 22 5 -1 z 1 30517578125 z 17 5 -1 17 -1 1 5 1354304952 -1 2 5 z 1 5 1 z 7 -1 1354304952 -1 3 5 1 -1 -1 3 5 z 1 5 z 7 -1 1354304952 -1 1 5 -1 4 5 z 1 5 1 z 7 -1 2257174920 -1 4 5 z 32 5 3968428464 -1 2 5 z 1 5 1 z 6 -1 3968428464 -1 3 5 1 -1 -1 3 5 z 1 5 z 6 -1 3968428464 -1 1 5 -1 4 5 z 1 5 1 z 6 -1 5767606845 -1 4 5 z 27 5 4072860792 -1 2 5 z 1 5 1 z 5 -1 4072860792 -1 3 5 1 -1 -1 3 5 z 1 5 z 5 -1 4072860792 -1 1 5 -1 4 5 z 1 5 1 z 5 -1 4828720050 -1 4 5 z 22 5 1645600320 -1 2 5 z 1 5 1 z 4 -1 1645600320 -1 3 5 1 -1 -1 3 5 z 1 5 z 4 -1 1645600320 -1 1 5 -1 4 5 z 1 5 1 z 4 -1 1347252025 -1 4 5 z 17 5 176314320 -1 2 5 z 1 5 1 z 3 -1 176314320 -1 3 5 1 -1 -1 3 5 z 1 5 z 3 -1 176314320 -1 1 5 -1 4 5 z 1 5 1 z 3 -1 23914800 -1 4 5 z 12 5 -1 9199008 -1 2 5 z 1 5 1 z 2 9199008 -1 3 5 1 -1 -1 3 5 z 1 5 z 2 9199008 -1 1 5 -1 4 5 z 1 5 1 z 2 3093480 -1 4 5 z 7 5 1192464 -1 2 5 z 1 5 1 z -1 1192464 -1 3 5 1 -1 -1 3 5 z 1 5 z -1 1192464 -1 1 5 -1 4 5 z 1 5 1 z -1 393120 -1 4 5 z 2 5 6552 -1 4 5 z 1 2 206701 z 5 192280 z 4 30360 z 3 -1 1840 z 2 230 z -24 z 1 5 1 6552 -1 2 5 z 1 2 206701 z 5 192280 z 4 30360 z 3 -1 1840 z 2 230 z -24 1 -1 -1 1 5 z 1 5 -1 157248 -1 2 5 z 1 5 1 157248 -1 3 5 1 -1 -1 3 5 z 1 5 157248 -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