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 BesselJ

 http://functions.wolfram.com/03.01.23.0007.01

 Input Form

 Sum[BesselJ[k, x]^2, {k, 1, Infinity}] == (1/2) (1 - BesselJ[0, x]^2)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], SuperscriptBox[RowBox[List["BesselJ", "[", RowBox[List["k", ",", "x"]], "]"]], "2"]]], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SuperscriptBox[RowBox[List["BesselJ", "[", RowBox[List["0", ",", "x"]], "]"]], "2"]]], ")"]]]]]]]]

 MathML Form

 k = 1 J k ( x ) 2 1 2 ( 1 - J 0 ( x ) 2 ) k 1 BesselJ k x 2 1 2 1 -1 BesselJ 0 x 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k_", "=", "1"]], "\[Infinity]"], SuperscriptBox[RowBox[List["BesselJ", "[", RowBox[List["k_", ",", "x_"]], "]"]], "2"]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SuperscriptBox[RowBox[List["BesselJ", "[", RowBox[List["0", ",", "x"]], "]"]], "2"]]], ")"]]]]]]]]

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

 2001-10-29