Sqrt[1 + z] == (-(1/(2 Sqrt[Pi]))) (1/(2 Pi I)) ContourIntegral[(Gamma[s] Gamma[-(1/2) - s])/z^s, \[ScriptCapitalL]["s"]]

Cell[BoxData[RowBox[List[SqrtBox[RowBox[List["1", "+", "z"]]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["1", RowBox[List["2", " ", SqrtBox["\[Pi]"]]]]]], FractionBox["1", RowBox[List["2", "\[Pi]", " ", "\[ImaginaryI]"]]], RowBox[List[SubscriptBox["\[Integral]", "\[ScriptCapitalL]"], RowBox[List[RowBox[List["Gamma", "[", "s", "]"]], RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "s"]], "]"]], " ", SuperscriptBox["z", RowBox[List["-", "s"]]], RowBox[List["\[DifferentialD]", "s"]]]]]]]]]]]]

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2001-10-29