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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(18/5), 3, 27/5, -z] == (1/(3417968750 z^(22/5))) (187 (-1)^(1/5) (835380 (-1)^(4/5) z^(2/5) + 2513160 (-1)^(4/5) z^(7/5) + 958230 (-1)^(4/5) z^(12/5) - 1474200 (-1)^(4/5) z^(17/5) - 10985450 (-1)^(4/5) z^(22/5) - 14902020 (-1)^(4/5) z^(27/5) - 8382465 (-1)^(4/5) z^(32/5) - 1758120 (-1)^(4/5) z^(37/5) + 6552 (-1)^(4/5) (1 + z)^6 (51 - 138 z + 161 z^2) Log[1 + z^(1/5)] + 6552 (-1)^(2/5) (1 + z)^6 (51 - 138 z + 161 z^2) Log[1 - (-1)^(1/5) z^(1/5)] + 334152 Log[1 + (-1)^(2/5) z^(1/5)] + 1100736 z Log[1 + (-1)^(2/5) z^(1/5)] + 642096 z^2 Log[1 + (-1)^(2/5) z^(1/5)] - 550368 z^3 Log[1 + (-1)^(2/5) z^(1/5)] + 2751840 z^4 Log[1 + (-1)^(2/5) z^(1/5)] + 9539712 z^5 Log[1 + (-1)^(2/5) z^(1/5)] + 10732176 z^6 Log[1 + (-1)^(2/5) z^(1/5)] + 5425056 z^7 Log[1 + (-1)^(2/5) z^(1/5)] + 1054872 z^8 Log[1 + (-1)^(2/5) z^(1/5)] - 334152 (-1)^(3/5) Log[1 - (-1)^(3/5) z^(1/5)] - 1100736 (-1)^(3/5) z Log[1 - (-1)^(3/5) z^(1/5)] - 642096 (-1)^(3/5) z^2 Log[1 - (-1)^(3/5) z^(1/5)] + 550368 (-1)^(3/5) z^3 Log[1 - (-1)^(3/5) z^(1/5)] - 2751840 (-1)^(3/5) z^4 Log[1 - (-1)^(3/5) z^(1/5)] - 9539712 (-1)^(3/5) z^5 Log[1 - (-1)^(3/5) z^(1/5)] - 10732176 (-1)^(3/5) z^6 Log[1 - (-1)^(3/5) z^(1/5)] - 5425056 (-1)^(3/5) z^7 Log[1 - (-1)^(3/5) z^(1/5)] - 1054872 (-1)^(3/5) z^8 Log[1 - (-1)^(3/5) z^(1/5)] - 334152 (-1)^(1/5) Log[1 + (-1)^(4/5) z^(1/5)] - 1100736 (-1)^(1/5) z Log[1 + (-1)^(4/5) z^(1/5)] - 642096 (-1)^(1/5) z^2 Log[1 + (-1)^(4/5) z^(1/5)] + 550368 (-1)^(1/5) z^3 Log[1 + (-1)^(4/5) z^(1/5)] - 2751840 (-1)^(1/5) z^4 Log[1 + (-1)^(4/5) z^(1/5)] - 9539712 (-1)^(1/5) z^5 Log[1 + (-1)^(4/5) z^(1/5)] - 10732176 (-1)^(1/5) z^6 Log[1 + (-1)^(4/5) z^(1/5)] - 5425056 (-1)^(1/5) z^7 Log[1 + (-1)^(4/5) z^(1/5)] - 1054872 (-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 , 3 ; 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["3", 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 3417968750 z 22 / 5 ( 187 - 1 5 ( 1054872 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 8 - 1054872 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 8 - 1054872 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 8 - 1758120 ( - 1 ) 4 / 5 z 37 / 5 + 5425056 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 7 - 5425056 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 7 - 5425056 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 7 - 8382465 ( - 1 ) 4 / 5 z 32 / 5 + 10732176 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 6 - 10732176 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 6 - 10732176 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 6 - 14902020 ( - 1 ) 4 / 5 z 27 / 5 + 9539712 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 5 - 9539712 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 5 - 9539712 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 5 - 10985450 ( - 1 ) 4 / 5 z 22 / 5 + 2751840 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 4 - 2751840 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 4 - 2751840 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 4 - 1474200 ( - 1 ) 4 / 5 z 17 / 5 - 550368 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 3 + 550368 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 3 + 550368 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 3 + 958230 ( - 1 ) 4 / 5 z 12 / 5 + 642096 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 2 - 642096 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 2 - 642096 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 2 + 2513160 ( - 1 ) 4 / 5 z 7 / 5 + 1100736 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z - 1100736 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z - 1100736 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z + 835380 ( - 1 ) 4 / 5 z 2 / 5 + 6552 ( - 1 ) 4 / 5 ( z + 1 ) 6 ( 161 z 2 - 138 z + 51 ) log ( z 5 + 1 ) + 6552 ( - 1 ) 2 / 5 ( z + 1 ) 6 ( 161 z 2 - 138 z + 51 ) log ( 1 - - 1 5 z 5 ) + 334152 log ( ( - 1 ) 2 / 5 z 5 + 1 ) - 334152 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) - 334152 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) ) HypergeometricPFQ -1 18 5 3 27 5 -1 z 1 3417968750 z 22 5 -1 187 -1 1 5 1054872 -1 2 5 z 1 5 1 z 8 -1 1054872 -1 3 5 1 -1 -1 3 5 z 1 5 z 8 -1 1054872 -1 1 5 -1 4 5 z 1 5 1 z 8 -1 1758120 -1 4 5 z 37 5 5425056 -1 2 5 z 1 5 1 z 7 -1 5425056 -1 3 5 1 -1 -1 3 5 z 1 5 z 7 -1 5425056 -1 1 5 -1 4 5 z 1 5 1 z 7 -1 8382465 -1 4 5 z 32 5 10732176 -1 2 5 z 1 5 1 z 6 -1 10732176 -1 3 5 1 -1 -1 3 5 z 1 5 z 6 -1 10732176 -1 1 5 -1 4 5 z 1 5 1 z 6 -1 14902020 -1 4 5 z 27 5 9539712 -1 2 5 z 1 5 1 z 5 -1 9539712 -1 3 5 1 -1 -1 3 5 z 1 5 z 5 -1 9539712 -1 1 5 -1 4 5 z 1 5 1 z 5 -1 10985450 -1 4 5 z 22 5 2751840 -1 2 5 z 1 5 1 z 4 -1 2751840 -1 3 5 1 -1 -1 3 5 z 1 5 z 4 -1 2751840 -1 1 5 -1 4 5 z 1 5 1 z 4 -1 1474200 -1 4 5 z 17 5 -1 550368 -1 2 5 z 1 5 1 z 3 550368 -1 3 5 1 -1 -1 3 5 z 1 5 z 3 550368 -1 1 5 -1 4 5 z 1 5 1 z 3 958230 -1 4 5 z 12 5 642096 -1 2 5 z 1 5 1 z 2 -1 642096 -1 3 5 1 -1 -1 3 5 z 1 5 z 2 -1 642096 -1 1 5 -1 4 5 z 1 5 1 z 2 2513160 -1 4 5 z 7 5 1100736 -1 2 5 z 1 5 1 z -1 1100736 -1 3 5 1 -1 -1 3 5 z 1 5 z -1 1100736 -1 1 5 -1 4 5 z 1 5 1 z 835380 -1 4 5 z 2 5 6552 -1 4 5 z 1 6 161 z 2 -1 138 z 51 z 1 5 1 6552 -1 2 5 z 1 6 161 z 2 -1 138 z 51 1 -1 -1 1 5 z 1 5 334152 -1 2 5 z 1 5 1 -1 334152 -1 3 5 1 -1 -1 3 5 z 1 5 -1 334152 -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