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 | | http://functions.wolfram.com/03.21.06.0033.01 | 
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 | | SphericalBesselJ[\[Nu], z]^2 \[Proportional] 
 ((2^(-2 - 2 \[Nu]) Pi z^(2 \[Nu]))/Gamma[3/2 + \[Nu]]^2) 
  (1 - z^2/(3 + 2 \[Nu]) + (z^4 (2 + \[Nu]))/((3 + 2 \[Nu])^2 
     (5 + 2 \[Nu])) + O[z^6]) | 
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 | | Cell[BoxData[RowBox[List[SuperscriptBox[RowBox[List["SphericalBesselJ", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "2"], "\[Proportional]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "\[Nu]"]]]]], " ", "\[Pi]", " ", SuperscriptBox["z", RowBox[List["2", " ", "\[Nu]"]]]]], SuperscriptBox[RowBox[List["Gamma", "[", RowBox[List[FractionBox["3", "2"], "+", "\[Nu]"]], "]"]], "2"]], RowBox[List["(", RowBox[List["1", "-", FractionBox[SuperscriptBox["z", "2"], RowBox[List["3", "+", RowBox[List["2", " ", "\[Nu]"]]]]], "+", FractionBox[RowBox[List[SuperscriptBox["z", "4"], " ", RowBox[List["(", RowBox[List["2", "+", "\[Nu]"]], ")"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["3", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]], "2"], " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]]], "+", RowBox[List["O", "[", SuperscriptBox["z", "6"], "]"]]]], ")"]]]]]]]] | 
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   <math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'>  <semantics>  <mrow>  <msup>  <mrow>  <msub>  <mi> j </mi>  <mi> ν </mi>  </msub>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  <mn> 2 </mn>  </msup>  <mo> ∝ </mo>  <mrow>  <mfrac>  <mrow>  <msup>  <mn> 2 </mn>  <mrow>  <mrow>  <mrow>  <mo> - </mo>  <mn> 2 </mn>  </mrow>  <mo> ⁢ </mo>  <mi> ν </mi>  </mrow>  <mo> - </mo>  <mn> 2 </mn>  </mrow>  </msup>  <mo> ⁢ </mo>  <mi> π </mi>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> ν </mi>  </mrow>  </msup>  </mrow>  <msup>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mi> ν </mi>  <mo> + </mo>  <mfrac>  <mn> 3 </mn>  <mn> 2 </mn>  </mfrac>  </mrow>  <mo> ) </mo>  </mrow>  <mn> 2 </mn>  </msup>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mfrac>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  <mrow>  <mn> 3 </mn>  <mo> + </mo>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> ν </mi>  </mrow>  </mrow>  </mfrac>  <mo> + </mo>  <mfrac>  <mrow>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 2 </mn>  <mo> + </mo>  <mi> ν </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mrow>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 3 </mn>  <mo> + </mo>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> ν </mi>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  <mn> 2 </mn>  </msup>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 5 </mn>  <mo> + </mo>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> ν </mi>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mfrac>  <mo> + </mo>  <mrow>  <mi> O </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <msup>  <mi> z </mi>  <mn> 6 </mn>  </msup>  <mo> ) </mo>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <ci> Proportional </ci>  <apply>  <power />  <apply>  <ci> SphericalBesselJ </ci>  <ci> ν </ci>  <ci> z </ci>  </apply>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <times />  <apply>  <times />  <apply>  <power />  <cn type='integer'> 2 </cn>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> -2 </cn>  <ci> ν </ci>  </apply>  <cn type='integer'> -2 </cn>  </apply>  </apply>  <pi />  <apply>  <power />  <ci> z </ci>  <apply>  <times />  <cn type='integer'> 2 </cn>  <ci> ν </ci>  </apply>  </apply>  <apply>  <power />  <apply>  <power />  <apply>  <ci> Gamma </ci>  <apply>  <plus />  <ci> ν </ci>  <cn type='rational'> 3 <sep /> 2 </cn>  </apply>  </apply>  <cn type='integer'> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <power />  <apply>  <plus />  <cn type='integer'> 3 </cn>  <apply>  <times />  <cn type='integer'> 2 </cn>  <ci> ν </ci>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 4 </cn>  </apply>  <apply>  <plus />  <cn type='integer'> 2 </cn>  <ci> ν </ci>  </apply>  <apply>  <power />  <apply>  <times />  <apply>  <power />  <apply>  <plus />  <cn type='integer'> 3 </cn>  <apply>  <times />  <cn type='integer'> 2 </cn>  <ci> ν </ci>  </apply>  </apply>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <plus />  <cn type='integer'> 5 </cn>  <apply>  <times />  <cn type='integer'> 2 </cn>  <ci> ν </ci>  </apply>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <ci> O </ci>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 6 </cn>  </apply>  </apply>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
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 | | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["SphericalBesselJ", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "2"], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "\[Nu]"]]]]], " ", "\[Pi]", " ", SuperscriptBox["z", RowBox[List["2", " ", "\[Nu]"]]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", FractionBox[SuperscriptBox["z", "2"], RowBox[List["3", "+", RowBox[List["2", " ", "\[Nu]"]]]]], "+", FractionBox[RowBox[List[SuperscriptBox["z", "4"], " ", RowBox[List["(", RowBox[List["2", "+", "\[Nu]"]], ")"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["3", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]], "2"], " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]]], "+", SuperscriptBox[RowBox[List["O", "[", "z", "]"]], "6"]]], ")"]]]], SuperscriptBox[RowBox[List["Gamma", "[", RowBox[List[FractionBox["3", "2"], "+", "\[Nu]"]], "]"]], "2"]]]]]] | 
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 | | Date Added to functions.wolfram.com (modification date) | 
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