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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.b0ov.01

 Input Form

 Hypergeometric2F1[9/5, 4, 19/5, -z] == (1/3125) (21 ((25 (7 + 2 z))/(1 + z)^2 - (1/z^(9/5)) (6 (5 z^(4/5) + 4 Log[1 + z^(1/5)] - 4 (-1)^(1/5) Log[1 - (-1)^(1/5) z^(1/5)] + 4 (-1)^(2/5) Log[1 + (-1)^(2/5) z^(1/5)] - 4 (-1)^(3/5) Log[1 - (-1)^(3/5) z^(1/5)] + 4 (-1)^(4/5) Log[1 + (-1)^(4/5) z^(1/5)])) + (1/z^(14/5)) (45 z^(4/5) - 20 z^(9/5) + 36 Log[1 + z^(1/5)] - 36 (-1)^(1/5) Log[1 - (-1)^(1/5) z^(1/5)] + 36 (-1)^(2/5) Log[1 + (-1)^(2/5) z^(1/5)] - 36 (-1)^(3/5) Log[1 - (-1)^(3/5) z^(1/5)] + 36 (-1)^(4/5) Log[1 + (-1)^(4/5) z^(1/5)])))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["9", "5"], ",", "4", ",", FractionBox["19", "5"], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "3125"], RowBox[List["(", RowBox[List["21", " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["25", " ", RowBox[List["(", RowBox[List["7", "+", RowBox[List["2", " ", "z"]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "2"]], "-", RowBox[List[FractionBox["1", SuperscriptBox["z", RowBox[List["9", "/", "5"]]]], RowBox[List["(", RowBox[List["6", " ", RowBox[List["(", RowBox[List[RowBox[List["5", " ", SuperscriptBox["z", RowBox[List["4", "/", "5"]]]]], "+", RowBox[List["4", " ", RowBox[List["Log", "[", RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], "]"]]]], "-", RowBox[List["4", " ", 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["1", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]], "+", RowBox[List["4", " ", 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["2", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]], "-", RowBox[List["4", " ", 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["3", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]], "+", RowBox[List["4", " ", 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["4", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]]]], ")"]]]], ")"]]]], "+", RowBox[List[FractionBox["1", SuperscriptBox["z", RowBox[List["14", "/", "5"]]]], RowBox[List["(", RowBox[List[RowBox[List["45", " ", SuperscriptBox["z", RowBox[List["4", "/", "5"]]]]], "-", RowBox[List["20", " ", SuperscriptBox["z", RowBox[List["9", "/", "5"]]]]], "+", RowBox[List["36", " ", RowBox[List["Log", "[", RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], "]"]]]], "-", RowBox[List["36", " ", 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["1", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]], "+", RowBox[List["36", " ", 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["2", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]], "-", RowBox[List["36", " ", 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["3", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]], "+", RowBox[List["36", " ", 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["4", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]]]], ")"]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( 9 5 , 4 ; 19 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["9", "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["19", "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 3125 ( 21 ( 25 ( 2 z + 7 ) ( z + 1 ) 2 - 1 z 9 / 5 ( 6 ( 4 log ( z 5 + 1 ) - 4 - 1 5 log ( 1 - - 1 5 z 5 ) + 4 ( - 1 ) 2 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) - 4 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) + 4 ( - 1 ) 4 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) + 5 z 4 / 5 ) ) + 1 z 14 / 5 ( - 20 z 9 / 5 + 45 z 4 / 5 + 36 log ( z 5 + 1 ) - 36 - 1 5 log ( 1 - - 1 5 z 5 ) + 36 ( - 1 ) 2 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) - 36 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) + 36 ( - 1 ) 4 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) ) ) HypergeometricPFQ 9 5 4 19 5 -1 z 1 3125 21 25 2 z 7 z 1 2 -1 -1 1 z 9 5 -1 6 4 z 1 5 1 -1 4 -1 1 5 1 -1 -1 1 5 z 1 5 4 -1 2 5 -1 2 5 z 1 5 1 -1 4 -1 3 5 1 -1 -1 3 5 z 1 5 4 -1 4 5 -1 4 5 z 1 5 1 5 z 4 5 1 z 14 5 -1 -20 z 9 5 45 z 4 5 36 z 1 5 1 -1 36 -1 1 5 1 -1 -1 1 5 z 1 5 36 -1 2 5 -1 2 5 z 1 5 1 -1 36 -1 3 5 1 -1 -1 3 5 z 1 5 36 -1 4 5 -1 4 5 z 1 5 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["9", "5"], ",", "4", ",", FractionBox["19", "5"], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["21", " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["25", " ", RowBox[List["(", RowBox[List["7", "+", RowBox[List["2", " ", "z"]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "2"]], "-", FractionBox[RowBox[List["6", " ", RowBox[List["(", RowBox[List[RowBox[List["5", " ", SuperscriptBox["z", RowBox[List["4", "/", "5"]]]]], "+", RowBox[List["4", " ", RowBox[List["Log", "[", RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], "]"]]]], "-", RowBox[List["4", " ", 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["1", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]], "+", RowBox[List["4", " ", 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["2", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]], "-", RowBox[List["4", " ", 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["3", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]], "+", RowBox[List["4", " ", 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["4", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]]]], ")"]]]], SuperscriptBox["z", RowBox[List["9", "/", "5"]]]], "+", FractionBox[RowBox[List[RowBox[List["45", " ", SuperscriptBox["z", RowBox[List["4", "/", "5"]]]]], "-", RowBox[List["20", " ", SuperscriptBox["z", RowBox[List["9", "/", "5"]]]]], "+", RowBox[List["36", " ", RowBox[List["Log", "[", RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], "]"]]]], "-", RowBox[List["36", " ", 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["1", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]], "+", RowBox[List["36", " ", 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["2", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]], "-", RowBox[List["36", " ", 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["3", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]], "+", RowBox[List["36", " ", 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["4", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]]]], SuperscriptBox["z", RowBox[List["14", "/", "5"]]]]]], ")"]]]], "3125"]]]]]

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

 2007-05-02