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variants of this functions
KelvinKer






Mathematica Notation

Traditional Notation









Bessel-Type Functions > KelvinKer[nu,z] > Differentiation > Symbolic differentiation > With respect to z





http://functions.wolfram.com/03.20.20.0013.01









  


  










Input Form





D[KelvinKer[\[Nu], z], {z, n}] == Sum[(-1)^(m + n) Binomial[n, m] Pochhammer[-\[Nu], n - m] Sum[(((-1)^k 2^(2 k - m) Pochhammer[-m, 2 (m - k)] Pochhammer[\[Nu], k])/ (m - k)!) (KelvinKer[\[Nu], z] Sum[(((-1)^j (k - 2 j)!)/ ((2 j)! (k - 4 j)! Pochhammer[1 - k - \[Nu], 2 j] Pochhammer[\[Nu], 2 j])) (z/2)^(4 j), {j, 0, Floor[k/2]}] + (z/(2 Sqrt[2])) (KelvinKei[-1 + \[Nu], z] + KelvinKer[-1 + \[Nu], z]) Sum[(((-1)^j (k - 2 j - 1)!)/((2 j)! (k - 4 j - 1)! Pochhammer[1 - k - \[Nu], 2 j] Pochhammer[\[Nu], 2 j + 1])) (z/2)^(4 j), {j, 0, Floor[(k - 1)/2]}] + (z^2/4) KelvinKei[\[Nu], z] Sum[(((-1)^j (k - 2 j - 1)!)/ ((2 j + 1)! (k - 4 j - 2)! Pochhammer[1 - k - \[Nu], 2 j + 1] Pochhammer[\[Nu], 2 j + 1])) (z/2)^(4 j), {j, 0, Floor[(k - 1)/2]}] + (z^3/(8 Sqrt[2])) (KelvinKei[-1 + \[Nu], z] - KelvinKer[-1 + \[Nu], z]) Sum[(((-1)^j (k - 2 j - 2)!)/((2 j + 1)! (k - 4 j - 3)! Pochhammer[1 - k - \[Nu], 2 j + 1] Pochhammer[\[Nu], 2 j + 2])) (z/2)^(4 j), {j, 0, Floor[(k - 2)/2]}]), {k, 0, m}], {m, 0, n}]/ z^n /; Element[n, Integers] && n >= 0










Standard Form





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RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]










MathML Form







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





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





2007-05-02





© 1998-2014 Wolfram Research, Inc.