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 BesselJ

 http://functions.wolfram.com/03.01.23.0005.01

 Input Form

 Sum[BesselJ[k, x] t^k, {k, -Infinity, Infinity}] == E^((1/2) x (t - 1/t))

 Standard Form

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

 MathML Form

 k = - J k ( x ) t k 1 2 x ( t - 1 t ) k -1 BesselJ k x t k 1 2 x t -1 1 t -1 [/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["BesselJ", "[", RowBox[List["k_", ",", "x_"]], "]"]], " ", SuperscriptBox["t_", "k_"]]]]], "]"]], "\[RuleDelayed]", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["1", "2"], " ", "x", " ", RowBox[List["(", RowBox[List["t", "-", FractionBox["1", "t"]]], ")"]]]]]]]]]

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

 2001-10-29

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