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 BesselJ

 http://functions.wolfram.com/03.01.07.0006.02

 Input Form

 BesselJ[n, z] == (1/Pi) Integrate[Cos[t n - z Sin[t]], {t, 0, Pi}] /; Element[n, Integers]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["BesselJ", "[", RowBox[List["n", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "\[Pi]"], RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Pi]"], RowBox[List[RowBox[List["Cos", "[", RowBox[List[RowBox[List["t", " ", "n"]], "-", RowBox[List["z", " ", RowBox[List["Sin", "[", "t", "]"]]]]]], "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]]]]]], "/;", RowBox[List["n", "\[Element]", "Integers"]]]]]]

 MathML Form

 J n ( z ) 1 π 0 π cos ( t n - z sin ( t ) ) t /; n Condition BesselJ n z 1 -1 t 0 t n -1 z t n [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BesselJ", "[", RowBox[List["n_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Pi]"], RowBox[List[RowBox[List["Cos", "[", RowBox[List[RowBox[List["t", " ", "n"]], "-", RowBox[List["z", " ", RowBox[List["Sin", "[", "t", "]"]]]]]], "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]], "\[Pi]"], "/;", RowBox[List["n", "\[Element]", "Integers"]]]]]]]]

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

 2001-10-29