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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.b0x8.01

 Input Form

 Hypergeometric2F1[2, 13/5, 23/5, -z] == (-(1872/125)) (-5 (1/(3 z^2) - 1/(8 z)) - (1/z^(13/5)) (-Log[1 + z^(1/5)] + E^((3 I Pi)/5) Log[1 - z^(1/5)/E^((I Pi)/5)] + Log[1 - E^((I Pi)/5) z^(1/5)]/ E^((3 I Pi)/5) + Log[1 - z^(1/5)/E^((3 I Pi)/5)]/E^((I Pi)/5) + E^((I Pi)/5) Log[1 - E^((3 I Pi)/5) z^(1/5)])) + (3042/125) (-5 (-(1/(3 z^3)) + 1/(8 z^2) - 1/(13 z)) - (1/z^(18/5)) (Log[1 + z^(1/5)] + Log[1 - z^(1/5)/E^((I Pi)/5)]/ E^((2 I Pi)/5) + E^((2 I Pi)/5) Log[1 - E^((I Pi)/5) z^(1/5)] + E^((4 I Pi)/5) Log[1 - z^(1/5)/E^((3 I Pi)/5)] + Log[1 - E^((3 I Pi)/5) z^(1/5)]/E^((4 I Pi)/5)))

 Standard Form

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 MathML Form

 2 F 1 ( 2 , 13 5 ; 23 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["13", "5"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["23", "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] 3042 125 ( - 5 ( - 1 13 z + 1 8 z 2 - 1 3 z 3 ) - 1 z 18 / 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 ) ) ) - 1872 125 ( - 5 ( 1 3 z 2 - 1 8 z ) - 1 z 13 / 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 13 5 23 5 -1 z 3042 125 -5 -1 1 13 z -1 1 8 z 2 -1 -1 1 3 z 3 -1 -1 1 z 18 5 -1 z 1 5 1 -1 2 5 -1 1 -1 -1 5 -1 z 1 5 2 5 -1 1 -1 5 -1 z 1 5 4 5 -1 1 -1 -1 3 5 -1 z 1 5 -1 4 5 -1 1 -1 3 5 -1 z 1 5 -1 1872 125 -5 1 3 z 2 -1 -1 1 8 z -1 -1 1 z 13 5 -1 -1 z 1 5 1 3 5 -1 1 -1 -1 5 -1 z 1 5 -1 3 5 -1 1 -1 5 -1 z 1 5 -1 5 -1 1 -1 -1 3 5 -1 z 1 5 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