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 BesselI

 http://functions.wolfram.com/03.02.06.0002.01

 Input Form

 BesselI[\[Nu], z] == Sum[(z/2)^(2 k + \[Nu])/(Gamma[k + \[Nu] + 1] k!), {k, 0, Infinity}]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["BesselI", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[SuperscriptBox[RowBox[List["(", FractionBox["z", "2"], ")"]], RowBox[List[RowBox[List["2", " ", "k"]], "+", "\[Nu]"]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List["k", "+", "\[Nu]", "+", "1"]], "]"]], " ", RowBox[List["k", "!"]]]]]]]]]]]

 MathML Form

 I ν ( z ) k = 0 1 Γ ( k + ν + 1 ) k ! ( z 2 ) 2 k + ν BesselI ν z k 0 1 Gamma k ν 1 k -1 z 2 -1 2 k ν [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BesselI", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[SuperscriptBox[RowBox[List["(", FractionBox["z", "2"], ")"]], RowBox[List[RowBox[List["2", " ", "k"]], "+", "\[Nu]"]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List["k", "+", "\[Nu]", "+", "1"]], "]"]], " ", RowBox[List["k", "!"]]]]]]]]]]]

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

 2001-10-29