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SphericalBesselJ




Mathematica Notation

Traditional Notation









Bessel-Type Functions > SphericalBesselJ[nu,z] > Representations through equivalent functions > With related functions





http://functions.wolfram.com/03.21.27.0004.01









  


  








Input Form





SphericalBesselJ[\[Nu], z] SphericalBesselY[1 + \[Nu], z] - SphericalBesselJ[1 + \[Nu], z] SphericalBesselY[\[Nu], z] == -(1/z^2)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List["SphericalBesselJ", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], " ", RowBox[List["SphericalBesselY", "[", RowBox[List[RowBox[List["1", "+", "\[Nu]"]], ",", "z"]], "]"]]]], "-", RowBox[List[RowBox[List["SphericalBesselJ", "[", RowBox[List[RowBox[List["1", "+", "\[Nu]"]], ",", "z"]], "]"]], " ", RowBox[List["SphericalBesselY", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]]]]]], "\[Equal]", RowBox[List["-", FractionBox["1", SuperscriptBox["z", "2"]]]]]]]]








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> <mrow> <msub> <mi> j </mi> <mi> &#957; </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> y </mi> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <msub> <mi> j </mi> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> y </mi> <mi> &#957; </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#63449; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <times /> <apply> <ci> SphericalBesselJ </ci> <ci> &#957; </ci> <ci> z </ci> </apply> <apply> <ci> SphericalBesselY </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> SphericalBesselJ </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <ci> z </ci> </apply> <apply> <ci> SphericalBesselY </ci> <ci> &#957; </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List[RowBox[List["SphericalBesselJ", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], " ", RowBox[List["SphericalBesselY", "[", RowBox[List[RowBox[List["1", "+", "\[Nu]_"]], ",", "z_"]], "]"]]]], "-", RowBox[List[RowBox[List["SphericalBesselJ", "[", RowBox[List[RowBox[List["1", "+", "\[Nu]_"]], ",", "z_"]], "]"]], " ", RowBox[List["SphericalBesselY", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox["1", SuperscriptBox["z", "2"]]]]]]]]


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





2007-05-02