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LogGamma






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > LogGamma[z] > Operations > Limit operation





http://functions.wolfram.com/06.11.25.0002.01









  


  










Input Form





Limit[LogGamma[x - I \[Epsilon]] - Log[Gamma[x - I \[Epsilon]]], \[Epsilon] -> 0] == 2 Pi I k /; Element[x, Reals] && Subscript[z, 2 k - 1] < x < Subscript[z, 2 k + 1] && PolyGamma[Subscript[z, k]] == 0 && 1.4 < Subscript[z, 0] < 1.5 && -0.6 < Subscript[z, 1] < -0.5 && -1.6 < Subscript[z, 2] < -1.5 && -2.7 < Subscript[z, 3] < -2.6 && -3.7 < Subscript[z, 4] < -3.6 && -4.7 < Subscript[z, 5] < -4.6 && -5.7 < Subscript[z, 6] < -5.6 && -6.7 < Subscript[z, 7] < -6.6 && \[Ellipsis] && Element[k, Integers] && k > 0










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Limit", "[", RowBox[List[RowBox[List[RowBox[List["LogGamma", "[", RowBox[List["x_", "-", RowBox[List["\[ImaginaryI]", " ", "\[Epsilon]_"]]]], "]"]], "-", RowBox[List["Log", "[", RowBox[List["Gamma", "[", RowBox[List["x_", "-", RowBox[List["\[ImaginaryI]", " ", "\[Epsilon]_"]]]], "]"]], "]"]]]], ",", RowBox[List["\[Epsilon]_", "\[Rule]", "0"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]", " ", "k"]], "/;", RowBox[List[RowBox[List["x", "\[Element]", "Reals"]], "&&", RowBox[List[SubscriptBox["z", RowBox[List[RowBox[List["2", " ", "k"]], "-", "1"]]], "<", "x", "<", SubscriptBox["z", RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]]]], "&&", RowBox[List[RowBox[List["PolyGamma", "[", SubscriptBox["z", "k"], "]"]], "\[Equal]", "0"]], "&&", RowBox[List["1.4`", "<", SubscriptBox["z", "0"], "<", "1.5`"]], "&&", RowBox[List[RowBox[List["-", "0.6`"]], "<", SubscriptBox["z", "1"], "<", RowBox[List["-", "0.5`"]]]], "&&", RowBox[List[RowBox[List["-", "1.6`"]], "<", SubscriptBox["z", "2"], "<", RowBox[List["-", "1.5`"]]]], "&&", RowBox[List[RowBox[List["-", "2.7`"]], "<", SubscriptBox["z", "3"], "<", RowBox[List["-", "2.6`"]]]], "&&", RowBox[List[RowBox[List["-", "3.7`"]], "<", SubscriptBox["z", "4"], "<", RowBox[List["-", "3.6`"]]]], "&&", RowBox[List[RowBox[List["-", "4.7`"]], "<", SubscriptBox["z", "5"], "<", RowBox[List["-", "4.6`"]]]], "&&", RowBox[List[RowBox[List["-", "5.7`"]], "<", SubscriptBox["z", "6"], "<", RowBox[List["-", "5.6`"]]]], "&&", RowBox[List[RowBox[List["-", "6.7`"]], "<", SubscriptBox["z", "7"], "<", RowBox[List["-", "6.6`"]]]], "&&", "\[Ellipsis]", "&&", RowBox[List["k", "\[Element]", "Integers"]], "&&", RowBox[List["k", ">", "0"]]]]]]]]]]










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





2007-05-02





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