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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.ayb6.01

 Input Form

 Hypergeometric2F1[2/5, 6, 12/5, -z] == (1/781250) (7 ((25 (2258 + 5214 z + 4329 z^2 + 1248 z^3))/(1 + z)^4 - (1/z^(2/5)) (21528 (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)])) + (1/z^(7/5)) (936 (5 z^(2/5) + 2 Log[1 + z^(1/5)] - 2 (-1)^(3/5) Log[1 - (-1)^(1/5) z^(1/5)] - 2 (-1)^(1/5) Log[1 + (-1)^(2/5) z^(1/5)] + 2 (-1)^(4/5) Log[1 - (-1)^(3/5) z^(1/5)] + 2 (-1)^(2/5) Log[1 + (-1)^(4/5) z^(1/5)]))))

 Standard Form

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 MathML Form

 2 F 1 ( 2 5 , 6 ; 12 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["6", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["12", "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 781250 ( 7 ( 25 ( 1248 z 3 + 4329 z 2 + 5214 z + 2258 ) ( z + 1 ) 4 - 1 z 2 / 5 ( 21528 ( 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 ) ) ) + 1 z 7 / 5 ( 936 ( 2 log ( z 5 + 1 ) - 2 ( - 1 ) 3 / 5 log ( 1 - - 1 5 z 5 ) - 2 - 1 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) + 2 ( - 1 ) 4 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) + 2 ( - 1 ) 2 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) + 5 z 2 / 5 ) ) ) ) HypergeometricPFQ 2 5 6 12 5 -1 z 1 781250 7 25 1248 z 3 4329 z 2 5214 z 2258 z 1 4 -1 -1 1 z 2 5 -1 21528 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 1 z 7 5 -1 936 2 z 1 5 1 -1 2 -1 3 5 1 -1 -1 1 5 z 1 5 -1 2 -1 1 5 -1 2 5 z 1 5 1 2 -1 4 5 1 -1 -1 3 5 z 1 5 2 -1 2 5 -1 4 5 z 1 5 1 5 z 2 5 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["2", "5"], ",", "6", ",", FractionBox["12", "5"], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["7", " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["25", " ", RowBox[List["(", RowBox[List["2258", "+", RowBox[List["5214", " ", "z"]], "+", RowBox[List["4329", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1248", " ", SuperscriptBox["z", "3"]]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "4"]], "-", FractionBox[RowBox[List["21528", " ", 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"]]]]]]], "]"]]]]]], ")"]]]], SuperscriptBox["z", RowBox[List["2", "/", "5"]]]], "+", FractionBox[RowBox[List["936", " ", RowBox[List["(", RowBox[List[RowBox[List["5", " ", SuperscriptBox["z", RowBox[List["2", "/", "5"]]]]], "+", RowBox[List["2", " ", RowBox[List["Log", "[", RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], "]"]]]], "-", RowBox[List["2", " ", 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["2", " ", 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["2", " ", 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["2", " ", 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"]]]]]]], "]"]]]]]], ")"]]]], SuperscriptBox["z", RowBox[List["7", "/", "5"]]]]]], ")"]]]], "781250"]]]]]

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

 2007-05-02