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 BesselI

 http://functions.wolfram.com/03.02.23.0015.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2001-10-29