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 Coth

 http://functions.wolfram.com/01.22.06.0008.01

 Input Form

 Coth[z] == 1 + 2 Sum[E^(-2 z (k + 1)), {k, 0, Infinity}] /; Re[z] > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Coth", "[", "z", "]"]], "\[Equal]", RowBox[List["1", "+", RowBox[List["2", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", "z", " ", RowBox[List["(", RowBox[List["k", "+", "1"]], ")"]]]]]]]]]]]]], "/;", " ", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ">", "0"]]]]]]

 MathML Form

 coth ( z ) 2 k = 0 - 2 z ( k + 1 ) + 1 /; Re ( z ) > 0 Condition z 2 k 0 -2 z k 1 1 z 0 [/itex]

 Rule Form

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

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

 2001-10-29

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