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 Cosh

 http://functions.wolfram.com/01.20.23.0003.01

 Input Form

 Sum[Cosh[(2 k - 1) a], {k, 1, n}] == (1/2) Csch[a] Sinh[2 n a]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "n"], RowBox[List["Cosh", "[", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "1"]], ")"]], " ", "a"]], "]"]]]], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["Csch", "[", "a", "]"]], " ", RowBox[List["Sinh", "[", RowBox[List["2", " ", "n", " ", "a"]], "]"]]]]]]]]

 MathML Form

 k = 1 n cosh ( ( 2 k - 1 ) a ) 1 2 csch ( a ) sinh ( 2 n a ) k 1 n 2 k -1 a 1 2 a 2 n a [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k_", "=", "1"]], "n_"], RowBox[List["Cosh", "[", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k_"]], "-", "1"]], ")"]], " ", "a_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["Csch", "[", "a", "]"]], " ", RowBox[List["Sinh", "[", RowBox[List["2", " ", "n", " ", "a"]], "]"]]]]]]]]

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

 2001-10-29