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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.ay6e.01

 Input Form

 Hypergeometric2F1[2/5, 4, 27/5, z] == (1/(1171875 z^(22/5))) (1309 (-1)^(1/5) (-3570 (-1)^(4/5) z^(2/5) + 660 (-1)^(4/5) z^(7/5) + 515 (-1)^(4/5) z^(12/5) + 520 (-1)^(4/5) z^(17/5) + 12 (-1)^(4/5) (-119 + 56 z + 21 z^2 + 16 z^3 + 26 z^4) Log[1 - z^(1/5)] + 12 (-1)^(2/5) (-119 + 56 z + 21 z^2 + 16 z^3 + 26 z^4) Log[1 + (-1)^(1/5) z^(1/5)] - 1428 Log[1 - (-1)^(2/5) z^(1/5)] + 672 z Log[1 - (-1)^(2/5) z^(1/5)] + 252 z^2 Log[1 - (-1)^(2/5) z^(1/5)] + 192 z^3 Log[1 - (-1)^(2/5) z^(1/5)] + 312 z^4 Log[1 - (-1)^(2/5) z^(1/5)] + 1428 (-1)^(3/5) Log[1 + (-1)^(3/5) z^(1/5)] - 672 (-1)^(3/5) z Log[1 + (-1)^(3/5) z^(1/5)] - 252 (-1)^(3/5) z^2 Log[1 + (-1)^(3/5) z^(1/5)] - 192 (-1)^(3/5) z^3 Log[1 + (-1)^(3/5) z^(1/5)] - 312 (-1)^(3/5) z^4 Log[1 + (-1)^(3/5) z^(1/5)] + 1428 (-1)^(1/5) Log[1 - (-1)^(4/5) z^(1/5)] - 672 (-1)^(1/5) z Log[1 - (-1)^(4/5) z^(1/5)] - 252 (-1)^(1/5) z^2 Log[1 - (-1)^(4/5) z^(1/5)] - 192 (-1)^(1/5) z^3 Log[1 - (-1)^(4/5) z^(1/5)] - 312 (-1)^(1/5) z^4 Log[1 - (-1)^(4/5) z^(1/5)]))

 Standard Form

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 MathML Form

 2 F 1 ( 2 5 , 4 ; 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[FractionBox["2", "5"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["4", 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["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 1171875 z 22 / 5 ( 1309 - 1 5 ( 312 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 4 - 312 ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 4 - 312 - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 4 + 520 ( - 1 ) 4 / 5 z 17 / 5 + 192 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 3 - 192 ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 3 - 192 - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 3 + 515 ( - 1 ) 4 / 5 z 12 / 5 + 252 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 2 - 252 ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 2 - 252 - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 2 + 660 ( - 1 ) 4 / 5 z 7 / 5 + 672 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z - 672 ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z - 672 - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z - 3570 ( - 1 ) 4 / 5 z 2 / 5 + 12 ( - 1 ) 4 / 5 ( 26 z 4 + 16 z 3 + 21 z 2 + 56 z - 119 ) log ( 1 - z 5 ) + 12 ( - 1 ) 2 / 5 ( 26 z 4 + 16 z 3 + 21 z 2 + 56 z - 119 ) log ( - 1 5 z 5 + 1 ) - 1428 log ( 1 - ( - 1 ) 2 / 5 z 5 ) + 1428 ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) + 1428 - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) ) HypergeometricPFQ 2 5 4 27 5 z 1 1171875 z 22 5 -1 1309 -1 1 5 312 1 -1 -1 2 5 z 1 5 z 4 -1 312 -1 3 5 -1 3 5 z 1 5 1 z 4 -1 312 -1 1 5 1 -1 -1 4 5 z 1 5 z 4 520 -1 4 5 z 17 5 192 1 -1 -1 2 5 z 1 5 z 3 -1 192 -1 3 5 -1 3 5 z 1 5 1 z 3 -1 192 -1 1 5 1 -1 -1 4 5 z 1 5 z 3 515 -1 4 5 z 12 5 252 1 -1 -1 2 5 z 1 5 z 2 -1 252 -1 3 5 -1 3 5 z 1 5 1 z 2 -1 252 -1 1 5 1 -1 -1 4 5 z 1 5 z 2 660 -1 4 5 z 7 5 672 1 -1 -1 2 5 z 1 5 z -1 672 -1 3 5 -1 3 5 z 1 5 1 z -1 672 -1 1 5 1 -1 -1 4 5 z 1 5 z -1 3570 -1 4 5 z 2 5 12 -1 4 5 26 z 4 16 z 3 21 z 2 56 z -119 1 -1 z 1 5 12 -1 2 5 26 z 4 16 z 3 21 z 2 56 z -119 -1 1 5 z 1 5 1 -1 1428 1 -1 -1 2 5 z 1 5 1428 -1 3 5 -1 3 5 z 1 5 1 1428 -1 1 5 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