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 BesselI

 http://functions.wolfram.com/03.02.11.0002.01

 Input Form

 Sum[BesselI[k, z] E^(I k q), {k, -Infinity, Infinity}] == E^(z Cos[q])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", RowBox[List["-", "\[Infinity]"]]]], "\[Infinity]"], RowBox[List[RowBox[List["BesselI", "[", RowBox[List["k", ",", "z"]], "]"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "k", " ", "q"]]]]]]], "\[Equal]", SuperscriptBox["\[ExponentialE]", RowBox[List["z", " ", RowBox[List["Cos", "[", "q", "]"]]]]]]]]]

 MathML Form

 k = - I k ( z ) k q z cos ( q ) k -1 BesselI k z k q z q [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k_", "=", RowBox[List["-", "\[Infinity]"]]]], "\[Infinity]"], RowBox[List[RowBox[List["BesselI", "[", RowBox[List["k_", ",", "z_"]], "]"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "k_", " ", "q_"]]]]]]], "]"]], "\[RuleDelayed]", SuperscriptBox["\[ExponentialE]", RowBox[List["z", " ", RowBox[List["Cos", "[", "q", "]"]]]]]]]]]

 Contributed by

 P. Abbott

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

 2007-05-02