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BesselK






Mathematica Notation

Traditional Notation









Bessel-Type Functions > BesselK[nu,z] > Series representations > Generalized power series > Expansions at z==0 > For the function itself > General case





http://functions.wolfram.com/03.04.06.0029.01









  


  










Input Form





BesselK[\[Nu], z] \[Proportional] (1/2) ((Gamma[\[Nu]] (1 + z^2/(4 (1 - \[Nu])) + z^4/(32 (1 - \[Nu]) (2 - \[Nu])) + O[z^6]))/(z/2)^\[Nu] + Gamma[-\[Nu]] (z/2)^\[Nu] (1 + z^2/(4 (\[Nu] + 1)) + z^4/(32 (\[Nu] + 1) (\[Nu] + 2)) + O[z^6])) /; !Element[\[Nu], Integers]










Standard Form





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MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msub> <mi> K </mi> <mi> &#957; </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> &#957; </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> &#957; </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mrow> <mtext> </mtext> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#957; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> + </mo> <mfrac> <msup> <mi> z </mi> <mn> 4 </mn> </msup> <mrow> <mn> 32 </mn> <mo> &#8290; 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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BesselK", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Gamma", "[", "\[Nu]", "]"]], " ", SuperscriptBox[RowBox[List["(", FractionBox["z", "2"], ")"]], RowBox[List["-", "\[Nu]"]]], " ", RowBox[List["(", RowBox[List["1", "+", FractionBox[SuperscriptBox["z", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["1", "-", "\[Nu]"]], ")"]]]]], "+", FractionBox[SuperscriptBox["z", "4"], RowBox[List["32", " ", RowBox[List["(", RowBox[List["1", "-", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List["2", "-", "\[Nu]"]], ")"]]]]], "+", SuperscriptBox[RowBox[List["O", "[", "z", "]"]], "6"]]], ")"]]]], "+", RowBox[List[RowBox[List["Gamma", "[", RowBox[List["-", "\[Nu]"]], "]"]], " ", SuperscriptBox[RowBox[List["(", FractionBox["z", "2"], ")"]], "\[Nu]"], " ", RowBox[List["(", RowBox[List["1", "+", FractionBox[SuperscriptBox["z", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["\[Nu]", "+", "1"]], ")"]]]]], "+", FractionBox[SuperscriptBox["z", "4"], RowBox[List["32", " ", RowBox[List["(", RowBox[List["\[Nu]", "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["\[Nu]", "+", "2"]], ")"]]]]], "+", SuperscriptBox[RowBox[List["O", "[", "z", "]"]], "6"]]], ")"]]]]]], ")"]]]], "/;", RowBox[List["!", RowBox[List["\[Nu]", "\[Element]", "Integers"]]]]]]]]]]










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





2007-05-02