html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Sech

 http://functions.wolfram.com/01.24.23.0004.01

 Input Form

 Sum[(1/2^(2 k)) Sech[z/2^k]^2, {k, 1, Infinity}] == -Csch[z]^2 + 1/z^2

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List[FractionBox["1", SuperscriptBox["2", RowBox[List["2", " ", "k"]]]], SuperscriptBox[RowBox[List["Sech", "[", FractionBox["z", SuperscriptBox["2", "k"]], "]"]], "2"]]]]], "\[Equal]", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["Csch", "[", "z", "]"]], "2"]]], "+", FractionBox["1", SuperscriptBox["z", "2"]]]]]]]]

 MathML Form

 k = 1 1 2 2 k sech 2 ( z 2 k ) 1 z 2 - csch 2 ( z ) k 1 1 2 2 k -1 z 2 k -1 2 1 z 2 -1 -1 z 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k_", "=", "1"]], "\[Infinity]"], FractionBox[SuperscriptBox[RowBox[List["Sech", "[", FractionBox["z_", SuperscriptBox["2", "k_"]], "]"]], "2"], SuperscriptBox["2", RowBox[List["2", " ", "k_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["Csch", "[", "z", "]"]], "2"]]], "+", FractionBox["1", SuperscriptBox["z", "2"]]]]]]]]

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

 2007-05-02