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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.b10h.01

 Input Form

 Hypergeometric2F1[2, 17/5, 27/5, -z] == (-(4488/125)) (-5 (-(1/(2 z^3)) + 1/(7 z^2) - 1/(12 z)) - (1/z^(17/5)) (-Log[1 + z^(1/5)] + Log[1 - z^(1/5)/E^((I Pi)/5)]/ E^((3 I Pi)/5) + E^((3 I Pi)/5) Log[1 - E^((I Pi)/5) z^(1/5)] + E^((I Pi)/5) Log[1 - z^(1/5)/E^((3 I Pi)/5)] + Log[1 - E^((3 I Pi)/5) z^(1/5)]/E^((I Pi)/5))) + (6358/125) (-5 (1/(2 z^4) - 1/(7 z^3) + 1/(12 z^2) - 1/(17 z)) - (1/z^(22/5)) (Log[1 + z^(1/5)] + E^((2 I Pi)/5) Log[1 - z^(1/5)/E^((I Pi)/5)] + Log[1 - E^((I Pi)/5) z^(1/5)]/ E^((2 I Pi)/5) + Log[1 - z^(1/5)/E^((3 I Pi)/5)]/E^((4 I Pi)/5) + E^((4 I Pi)/5) Log[1 - E^((3 I Pi)/5) z^(1/5)]))

 Standard Form

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 MathML Form

 2 F 1 ( 2 , 17 5 ; 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["2", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["17", "5"], 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] 6358 125 ( - 5 ( - 1 17 z + 1 12 z 2 - 1 7 z 3 + 1 2 z 4 ) - 1 z 22 / 5 ( log ( z 5 + 1 ) + 2 π 5 log ( 1 - - π 5 z 5 ) + - 2 π 5 log ( 1 - π 5 z 5 ) + - 4 π 5 log ( 1 - - 3 π 5 z 5 ) + 4 π 5 log ( 1 - 3 π 5 z 5 ) ) ) - 4488 125 ( - 5 ( - 1 12 z + 1 7 z 2 - 1 2 z 3 ) - 1 z 17 / 5 ( - log ( z 5 + 1 ) + - 3 π 5 log ( 1 - - π 5 z 5 ) + 3 π 5 log ( 1 - π 5 z 5 ) + π 5 log ( 1 - - 3 π 5 z 5 ) + - π 5 log ( 1 - 3 π 5 z 5 ) ) ) HypergeometricPFQ 2 17 5 27 5 -1 z 6358 125 -5 -1 1 17 z -1 1 12 z 2 -1 -1 1 7 z 3 -1 1 2 z 4 -1 -1 1 z 22 5 -1 z 1 5 1 2 5 -1 1 -1 -1 5 -1 z 1 5 -1 2 5 -1 1 -1 5 -1 z 1 5 -1 4 5 -1 1 -1 -1 3 5 -1 z 1 5 4 5 -1 1 -1 3 5 -1 z 1 5 -1 4488 125 -5 -1 1 12 z -1 1 7 z 2 -1 -1 1 2 z 3 -1 -1 1 z 17 5 -1 -1 z 1 5 1 -1 3 5 -1 1 -1 -1 5 -1 z 1 5 3 5 -1 1 -1 5 -1 z 1 5 5 -1 1 -1 -1 3 5 -1 z 1 5 -1 5 -1 1 -1 3 5 -1 z 1 5 [/itex]

 Rule Form

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

 2007-05-02