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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(13/5), 5, -(3/5), -z] == (1/46875) (26 ((25 (1131 + 2072 z + 966 z^2))/(1 + z)^3 - 75348 (-(5/8) + (5 z)/3 - z^(8/5) (Log[1 + z^(1/5)] - (-1)^(3/5) Log[1 - (-1)^(1/5) z^(1/5)] - (-1)^(1/5) Log[1 + (-1)^(2/5) z^(1/5)] + (-1)^(4/5) Log[1 - (-1)^(3/5) z^(1/5)] + (-1)^(2/5) Log[1 + (-1)^(4/5) z^(1/5)])) + 191268 (-(5/13) + (5 z)/8 - (5 z^2)/3 + z^(13/5) (Log[1 + z^(1/5)] - (-1)^(3/5) Log[1 - (-1)^(1/5) z^(1/5)] - (-1)^(1/5) Log[1 + (-1)^(2/5) z^(1/5)] + (-1)^(4/5) Log[1 - (-1)^(3/5) z^(1/5)] + (-1)^(2/5) Log[1 + (-1)^(4/5) z^(1/5)]))))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["13", "5"]]], ",", "5", ",", RowBox[List["-", FractionBox["3", "5"]]], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "46875"], RowBox[List["(", RowBox[List["26", " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["25", " ", RowBox[List["(", RowBox[List["1131", "+", RowBox[List["2072", " ", "z"]], "+", RowBox[List["966", " ", SuperscriptBox["z", "2"]]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "3"]], "-", RowBox[List["75348", " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox["5", "8"]]], "+", FractionBox[RowBox[List["5", " ", "z"]], "3"], "-", RowBox[List[SuperscriptBox["z", RowBox[List["8", "/", "5"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], "]"]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "5"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "5"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["2", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["4", "/", "5"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["2", "/", "5"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["4", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["191268", " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox["5", "13"]]], "+", FractionBox[RowBox[List["5", " ", "z"]], "8"], "-", FractionBox[RowBox[List["5", " ", SuperscriptBox["z", "2"]]], "3"], "+", RowBox[List[SuperscriptBox["z", RowBox[List["13", "/", "5"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], "]"]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "5"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "5"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["2", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["4", "/", "5"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["2", "/", "5"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["4", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( - 13 5 , 5 ; - 3 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["13", "5"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["5", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["-", FractionBox["3", "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 46875 ( 26 ( 25 ( 966 z 2 + 2072 z + 1131 ) ( z + 1 ) 3 - 75348 ( - ( log ( z 5 + 1 ) - ( - 1 ) 3 / 5 log ( 1 - - 1 5 z 5 ) - - 1 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) + ( - 1 ) 4 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) + ( - 1 ) 2 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) z 8 / 5 + 5 z 3 - 5 8 ) + 191268 ( ( log ( z 5 + 1 ) - ( - 1 ) 3 / 5 log ( 1 - - 1 5 z 5 ) - - 1 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) + ( - 1 ) 4 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) + ( - 1 ) 2 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) z 13 / 5 - 5 z 2 3 + 5 z 8 - 5 13 ) ) ) HypergeometricPFQ -1 13 5 5 -1 3 5 -1 z 1 46875 26 25 966 z 2 2072 z 1131 z 1 3 -1 -1 75348 -1 z 1 5 1 -1 -1 3 5 1 -1 -1 1 5 z 1 5 -1 -1 1 5 -1 2 5 z 1 5 1 -1 4 5 1 -1 -1 3 5 z 1 5 -1 2 5 -1 4 5 z 1 5 1 z 8 5 5 z 3 -1 -1 5 8 191268 z 1 5 1 -1 -1 3 5 1 -1 -1 1 5 z 1 5 -1 -1 1 5 -1 2 5 z 1 5 1 -1 4 5 1 -1 -1 3 5 z 1 5 -1 2 5 -1 4 5 z 1 5 1 z 13 5 -1 5 z 2 3 -1 5 z 8 -1 -1 5 13 [/itex]

 Rule Form

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

 2007-05-02