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 Sinh

 http://functions.wolfram.com/01.19.23.0001.01

 Input Form

 Sum[Sinh[a k], {k, 0, n}] == Csch[a/2] Sinh[(1/2) a (n + 1)] Sinh[(a n)/2]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], RowBox[List["Sinh", "[", RowBox[List["a", " ", "k"]], "]"]]]], "\[Equal]", RowBox[List[RowBox[List["Csch", "[", FractionBox["a", "2"], "]"]], " ", RowBox[List["Sinh", "[", RowBox[List[FractionBox["1", "2"], " ", "a", " ", RowBox[List["(", RowBox[List["n", "+", "1"]], ")"]]]], "]"]], " ", RowBox[List["Sinh", "[", FractionBox[RowBox[List["a", " ", "n"]], "2"], "]"]]]]]]]]

 MathML Form

 k = 0 n sinh ( a k ) csch ( a 2 ) sinh ( a ( n + 1 ) 2 ) sinh ( a n 2 ) k 0 n a k a 2 -1 a n 1 2 -1 a n 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k_", "=", "0"]], "n_"], RowBox[List["Sinh", "[", RowBox[List["a_", " ", "k_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Csch", "[", FractionBox["a", "2"], "]"]], " ", RowBox[List["Sinh", "[", RowBox[List[FractionBox["1", "2"], " ", "a", " ", RowBox[List["(", RowBox[List["n", "+", "1"]], ")"]]]], "]"]], " ", RowBox[List["Sinh", "[", FractionBox[RowBox[List["a", " ", "n"]], "2"], "]"]]]]]]]]

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

 2001-10-29