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SphericalBesselJ






Mathematica Notation

Traditional Notation









Bessel-Type Functions > SphericalBesselJ[nu,z] > Identities > Recurrence identities > Distant neighbors > Increasing





http://functions.wolfram.com/03.21.17.0003.01









  


  










Input Form





SphericalBesselJ[\[Nu], z] == (2^(-1 + n) Pochhammer[3/2 + \[Nu], -1 + n] ((1 + 2 n + 2 \[Nu]) Sum[((n - k)! SphericalBesselJ[n + \[Nu], z] z^(2 k))/ (2^(2 k) (k! (n - 2 k)! Pochhammer[-(1/2) - n - \[Nu], k] Pochhammer[3/2 + \[Nu], k])), {k, 0, Floor[n/2]}] - z Sum[((n - k - 1)! SphericalBesselJ[1 + n + \[Nu], z] z^(2 k))/ (2^(2 k) (k! (n - 2 k - 1)! Pochhammer[1/2 - n - \[Nu], k] Pochhammer[3/2 + \[Nu], k])), {k, 0, Floor[(n - 1)/2]}]))/z^n










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> <msub> <mi> j </mi> <mi> &#957; </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <msup> <mn> 2 </mn> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mi> n </mi> </mrow> </msup> <mo> &#8290; </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> + </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[&quot;\[Nu]&quot;, &quot;+&quot;, FractionBox[&quot;3&quot;, &quot;2&quot;]]], &quot;)&quot;]], RowBox[List[&quot;n&quot;, &quot;-&quot;, &quot;1&quot;]]], Pochhammer] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; 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Rule Form





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





2007-05-02





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