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; }

 BesselI

 http://functions.wolfram.com/03.02.23.0002.01

 Input Form

 Sum[(-1)^k BesselI[k, x]^2, {k, 1, Infinity}] == (1/2) (1 - BesselI[0, x]^2)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", SuperscriptBox[RowBox[List["BesselI", "[", RowBox[List["k", ",", "x"]], "]"]], "2"]]]]], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SuperscriptBox[RowBox[List["BesselI", "[", RowBox[List["0", ",", "x"]], "]"]], "2"]]], ")"]]]]]]]]

 MathML Form

 k = 1 ( - 1 ) k I k ( x ) 2 1 2 ( 1 - I 0 ( x ) 2 ) k 1 -1 k BesselI k x 2 1 2 1 -1 BesselI 0 x 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k_", "=", "1"]], "\[Infinity]"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k_"], " ", SuperscriptBox[RowBox[List["BesselI", "[", RowBox[List["k_", ",", "x_"]], "]"]], "2"]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SuperscriptBox[RowBox[List["BesselI", "[", RowBox[List["0", ",", "x"]], "]"]], "2"]]], ")"]]]]]]]]

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

 2001-10-29