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 BesselJ

 http://functions.wolfram.com/03.01.23.0001.01

 Input Form

 Sum[(BesselJ[k + \[Nu], x] x^k)/k!, {k, 0, Infinity}] == BesselI[\[Nu], x]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["BesselJ", "[", RowBox[List[RowBox[List["k", "+", "\[Nu]"]], ",", "x"]], "]"]], " ", SuperscriptBox["x", "k"]]], RowBox[List["k", "!"]]]]], "\[Equal]", RowBox[List["BesselI", "[", RowBox[List["\[Nu]", ",", "x"]], "]"]]]]]]

 MathML Form

 k = 0 1 k ! J k + ν ( x ) x k I ν ( x ) k 0 1 k -1 BesselJ k ν x x k BesselI ν x [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k_", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["BesselJ", "[", RowBox[List[RowBox[List["k_", "+", "\[Nu]_"]], ",", "x_"]], "]"]], " ", SuperscriptBox["x_", "k_"]]], RowBox[List["k_", "!"]]]]], "]"]], "\[RuleDelayed]", RowBox[List["BesselI", "[", RowBox[List["\[Nu]", ",", "x"]], "]"]]]]]]

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

 2001-10-29