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; }

 EllipticK

 http://functions.wolfram.com/08.02.06.0016.01

 Input Form

 EllipticK[z] == (Pi/2) (1 + 4 Sum[EllipticNomeQ[z]^k/(EllipticNomeQ[z]^(2 k) + 1), {k, 1, Infinity}])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["EllipticK", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox["\[Pi]", "2"], RowBox[List["(", RowBox[List["1", "+", RowBox[List["4", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[SuperscriptBox[RowBox[List["EllipticNomeQ", "[", "z", "]"]], "k"], RowBox[List[SuperscriptBox[RowBox[List["EllipticNomeQ", "[", "z", "]"]], RowBox[List["2", " ", "k"]]], "+", "1"]]]]]]]]], ")"]]]]]]]]

 MathML Form

 K ( z ) π 2 ( 1 + 4 k = 1 q EllipticNomeQ ( z ) k q EllipticNomeQ ( z ) 2 k + 1 ) EllipticK z 2 -1 1 4 k 1 EllipticNomeQ z k EllipticNomeQ z 2 k 1 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticK", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["4", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[SuperscriptBox[RowBox[List["EllipticNomeQ", "[", "z", "]"]], "k"], RowBox[List[SuperscriptBox[RowBox[List["EllipticNomeQ", "[", "z", "]"]], RowBox[List["2", " ", "k"]]], "+", "1"]]]]]]]]], ")"]]]]]]]]

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

 2001-10-29