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 BesselK

 http://functions.wolfram.com/03.04.07.0007.01

 Input Form

 BesselK[0, x] == Integrate[Cos[x t]/Sqrt[t^2 + 1], {t, 0, Infinity}] /; x > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["BesselK", "[", RowBox[List["0", ",", "x"]], "]"]], "\[Equal]", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[FractionBox[RowBox[List["Cos", "[", RowBox[List["x", " ", "t"]], "]"]], SqrtBox[RowBox[List[SuperscriptBox["t", "2"], "+", "1"]]]], RowBox[List["\[DifferentialD]", "t"]]]]]]]], "/;", RowBox[List["x", ">", "0"]]]]]]

 MathML Form

 K 0 ( x ) 0 cos ( x t ) t 2 + 1 t /; x > 0 Condition BesselK 0 x t 0 x t t 2 1 1 2 -1 x 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BesselK", "[", RowBox[List["0", ",", "x_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[FractionBox[RowBox[List["Cos", "[", RowBox[List["x", " ", "t"]], "]"]], SqrtBox[RowBox[List[SuperscriptBox["t", "2"], "+", "1"]]]], RowBox[List["\[DifferentialD]", "t"]]]]]], "/;", RowBox[List["x", ">", "0"]]]]]]]]

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

 2001-10-29