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/01.24.06.0007.01

 Input Form

 Sech[z] == -2 Sum[(-1)^k q^(2 k - 1), {k, 1, Infinity}] /; q == E^z

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Sech", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", SuperscriptBox["q", RowBox[List[RowBox[List["2", " ", "k"]], "-", "1"]]]]]]]]]]], "/;", RowBox[List["q", "\[Equal]", SuperscriptBox["\[ExponentialE]", "z"]]]]]]]

 MathML Form

 sech ( z ) - 2 k = 1 ( - 1 ) k q 2 k - 1 /; q z Condition z -2 k 1 -1 k q 2 k -1 q z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Sech", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", SuperscriptBox["q", RowBox[List[RowBox[List["2", " ", "k"]], "-", "1"]]]]]]]]], "/;", RowBox[List["q", "\[Equal]", SuperscriptBox["\[ExponentialE]", "z"]]]]]]]]]

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

 2001-10-29