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 BesselJ

 http://functions.wolfram.com/03.01.06.0036.01

 Input Form

 BesselJ[\[Nu], z] == (1/Gamma[1 + \[Nu]]) (z/2)^\[Nu] Hypergeometric0F1[\[Nu] + 1, -(z^2/4)]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["BesselJ", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["Gamma", "[", RowBox[List["1", "+", "\[Nu]"]], "]"]]], SuperscriptBox[RowBox[List["(", FractionBox["z", RowBox[List[" ", "2"]]], ")"]], "\[Nu]"], RowBox[List["Hypergeometric0F1", "[", RowBox[List[RowBox[List["\[Nu]", " ", "+", " ", "1"]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", "2"], "4"]]]]], "]"]]]]]]]]

 MathML Form

 J ν ( z ) 1 Γ ( ν + 1 ) ( z 2 ) ν 0 F 1 ( ; ν + 1 ; - z 2 4 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["0", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox["\[Null]", InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric0F1, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["\[Nu]", "+", "1"]], Hypergeometric0F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric0F1, Rule[Editable, False]], ";", TagBox[RowBox[List["-", FractionBox[SuperscriptBox["z", "2"], "4"]]], Hypergeometric0F1, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric0F1] BesselJ ν z 1 Gamma ν 1 -1 z 2 -1 ν Hypergeometric0F1 ν 1 -1 z 2 4 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BesselJ", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["z", "2"], ")"]], "\[Nu]"], " ", RowBox[List["Hypergeometric0F1", "[", RowBox[List[RowBox[List["\[Nu]", "+", "1"]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", "2"], "4"]]]]], "]"]]]], RowBox[List["Gamma", "[", RowBox[List["1", "+", "\[Nu]"]], "]"]]]]]]]

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

 2007-05-02