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 Cot

 http://functions.wolfram.com/01.09.06.0009.01

 Input Form

 Cot[z] == I + 2 I Sum[E^(-2 I z (k + 1)), {k, 0, Infinity}] /; Im[z] < 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Cot", "[", "z", "]"]], "\[Equal]", RowBox[List["\[ImaginaryI]", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "z", " ", RowBox[List["(", RowBox[List["k", "+", "1"]], ")"]]]]]]]]]]]]], "/;", " ", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "<", "0"]]]]]]

 MathML Form

 cot ( z ) + 2 k = 0 - 2 z ( k + 1 ) /; Im ( z ) < 0 Condition z 2 k 0 -2 z k 1 z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Cot", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[ImaginaryI]", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "z", " ", RowBox[List["(", RowBox[List["k", "+", "1"]], ")"]]]]]]]]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "<", "0"]]]]]]]]

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

 2001-10-29