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 BesselJ

 http://functions.wolfram.com/03.01.11.0001.01

 Input Form

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

 Standard Form

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

 MathML Form

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

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

 2001-11-20