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variants of this functions
KelvinKer






Mathematica Notation

Traditional Notation









Bessel-Type Functions > KelvinKer[z] > Representations through more general functions > Through Meijer G > Classical cases involving 0F1





http://functions.wolfram.com/03.16.26.0027.01









  


  










Input Form





Hypergeometric0F1[1, (I z^2)/4] KelvinKer[z] == (1/8) Sqrt[Pi] (MeijerG[{{}, {}}, {{0, 0}, {0, 1/2}}, z^4/64] + I MeijerG[{{}, {}}, {{0, 1/2}, {0, 0}}, z^4/64] + (1/(Sqrt[2] Pi)) (MeijerG[{{1/4, 3/4}, {}}, {{0, 0, 1/2}, {0, 1/2, 1/2}}, z^4/16] - I MeijerG[{{1/4, 3/4}, {}}, {{0, 1/2, 1/2}, {0, 0, 1/2}}, z^4/16])) /; Inequality[-(Pi/4), Less, Arg[z], LessEqual, Pi/4]










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> <mrow> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mn> 0 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mo> &#8202; </mo> <mo> ; </mo> <mn> 1 </mn> <mo> ; </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mn> 4 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, &quot;0&quot;], SubscriptBox[&quot;F&quot;, &quot;1&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[&quot;\[Null]&quot;, InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric0F1, Rule[Editable, False], Rule[Selectable, False]], &quot;;&quot;, TagBox[TagBox[TagBox[&quot;1&quot;, Hypergeometric0F1, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric0F1, Rule[Editable, False], Rule[Selectable, False]], &quot;;&quot;, TagBox[FractionBox[RowBox[List[&quot;\[ImaginaryI]&quot;, &quot; 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Rule Form





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





2007-05-02