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variants of this functions
KelvinKei






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/03.19.27.0010.01









  


  










Input Form





KelvinKei[\[Nu], z] + I KelvinKer[\[Nu], z] == Piecewise[{{(-((Pi I)/2)) (BesselY[\[Nu], (-1)^(1/4) z]/E^(I Pi \[Nu]) + (3 I Cos[Pi \[Nu]] - Sin[Pi \[Nu]]) BesselJ[\[Nu], (-1)^(1/4) z]), Inequality[(3 Pi)/4, Less, Arg[z], LessEqual, Pi]}}, (-((Pi I E^(I Pi \[Nu]))/2)) (BesselY[\[Nu], (-1)^(1/4) z] - I BesselJ[\[Nu], (-1)^(1/4) z])] /; Element[\[Nu], Integers]










Standard Form





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MathML Form







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</mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mtd> <mtd> <semantics> <mi> True </mi> <annotation encoding='Mathematica'> TagBox[&quot;True&quot;, &quot;PiecewiseDefault&quot;, Rule[AutoDelete, False], Rule[DeletionWarning, True]] </annotation> </semantics> </mtd> </mtr> </mtable> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> &#957; </mi> <mo> &#8712; </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> <plus /> <apply> <ci> KelvinKei </ci> <ci> &#957; </ci> <ci> z </ci> </apply> <apply> <times /> <imaginaryi /> <apply> <ci> KelvinKer </ci> <ci> &#957; </ci> <ci> z </ci> </apply> </apply> </apply> <piecewise> <piece> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <pi /> <imaginaryi /> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <pi /> <ci> &#957; </ci> </apply> </apply> <apply> <ci> BesselY </ci> <ci> &#957; </ci> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <imaginaryi /> <apply> <cos /> <apply> <times /> <pi /> <ci> &#957; </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <sin /> <apply> <times /> <pi /> <ci> &#957; </ci> </apply> </apply> </apply> </apply> <apply> <ci> BesselJ </ci> <ci> &#957; </ci> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <ci> Inequality </ci> <apply> <times /> <cn type='integer'> 3 </cn> <pi /> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <lt /> <apply> <arg /> <ci> z </ci> </apply> <leq /> <pi /> </apply> </piece> <otherwise> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <pi /> <imaginaryi /> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <pi /> <ci> &#957; </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <ci> BesselY </ci> <ci> &#957; </ci> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <ci> BesselJ </ci> <ci> &#957; </ci> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </otherwise> </piecewise> </apply> <apply> <in /> <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