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variants of this functions
KelvinKei






Mathematica Notation

Traditional Notation









Bessel-Type Functions > KelvinKei[nu,z] > Differentiation > Low-order differentiation > With respect to nu





http://functions.wolfram.com/03.19.20.0001.01









  


  










Input Form





Derivative[1, 0][KelvinKei][\[Nu], z] == (Pi/2) ((-((3 Pi)/4)) Csc[Pi \[Nu]] KelvinBer[-\[Nu], z] + (1/4) (Pi - 8 Cot[Pi \[Nu]] Log[z/2]) KelvinBei[\[Nu], z] - (2/Pi) (Pi Cot[Pi \[Nu]] + Log[z/2]) KelvinKei[\[Nu], z] + ((1/4) Pi Cot[Pi \[Nu]] + 2 Log[z/2]) KelvinBer[\[Nu], z] + (2^\[Nu] Csc[Pi \[Nu]] Sum[(z^(2 k) PolyGamma[1 + k - \[Nu]] Sin[(1/4) Pi (2 k - 3 \[Nu])])/(2^(2 k) (k! Gamma[1 + k - \[Nu]])), {k, 0, Infinity}])/z^\[Nu] + (z^\[Nu] Csc[Pi \[Nu]] Sum[((z^(2 k) PolyGamma[1 + k + \[Nu]])/ (2^(2 k) (k! Gamma[1 + k + \[Nu]]))) Sin[(1/4) Pi (2 k - \[Nu])], {k, 0, Infinity}])/2^\[Nu]) /; !Element[\[Nu], Integers]










Standard Form





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MathML Form







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</mo> <mrow> <msub> <mi> bei </mi> <mi> &#957; </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> &#957; </mi> <mo> &#8713; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[List[], Integers]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 1 </cn> <cn type='integer'> 0 </cn> </list> <apply> <ci> Subscript </ci> <apply> <ci> BesselI </ci> <ci> kei </ci> </apply> <ci> &#957; </ci> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <pi /> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> <apply> <csc /> <apply> <times /> <pi /> <ci> &#957; </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; 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</ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <factorial /> <ci> k </ci> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> k </ci> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 3 </cn> <pi /> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <csc /> <apply> <times /> <pi /> <ci> &#957; </ci> </apply> </apply> <apply> <ci> KelvinBer </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <pi /> <apply> <cot /> <apply> <times /> <pi /> <ci> &#957; 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</ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <notin /> <ci> &#957; </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02





© 1998-2014 Wolfram Research, Inc.