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variants of this functions
KelvinKei






Mathematica Notation

Traditional Notation









Bessel-Type Functions > KelvinKei[nu,z] > Series representations > Generalized power series > Expansions at generic point z==z0





http://functions.wolfram.com/03.19.06.0005.01









  


  










Input Form





KelvinKei[\[Nu], z] == (-(1/4)) Sum[(1/k!) MeijerG[{{-(k/4), (1 - k)/4, (2 - k)/4, (3 - k)/4}, {(2 \[Nu] - k)/4}}, {{(\[Nu] + k - n)/4, (\[Nu] - k)/4, (2 - \[Nu] - k)/4, -((\[Nu] + k)/4)}, {(2 \[Nu] - k)/4, 0, 1/4, 1/2, 3/4}}, Subscript[z, 0]/4, 1/4] (z - Subscript[z, 0])^k, {k, 0, Infinity}] /; Abs[Arg[Subscript[z, 0]]] < Pi










Standard Form





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MathML Form







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</mo> <mi> &#957; </mi> </mrow> <mo> - </mo> <mi> k </mi> </mrow> <mn> 4 </mn> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> k </mi> <mo> - </mo> <mi> n </mi> <mo> + </mo> <mi> &#957; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mfrac> <mrow> <mi> &#957; </mi> <mo> - </mo> <mi> k </mi> </mrow> <mn> 4 </mn> </mfrac> <mo> , </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> - </mo> <mi> k </mi> <mo> - </mo> <mi> &#957; </mi> </mrow> <mn> 4 </mn> </mfrac> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> k </mi> <mo> + </mo> <mi> &#957; </mi> </mrow> <mn> 4 </mn> </mfrac> </mrow> <mo> , </mo> <mfrac> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> - </mo> <mi> k </mi> </mrow> <mn> 4 </mn> </mfrac> <mo> , </mo> <mn> 0 </mn> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 3 </mn> <mn> 4 </mn> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox[&quot;G&quot;, MeijerG], RowBox[List[&quot;5&quot;, &quot;,&quot;, &quot;9&quot;]], RowBox[List[&quot;4&quot;, &quot;,&quot;, &quot;4&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[RowBox[List[TagBox[FractionBox[SubscriptBox[&quot;z&quot;, &quot;0&quot;], &quot;4&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;1&quot;, &quot;4&quot;], MeijerG, Rule[Editable, True]]]], MeijerG], &quot;\[VerticalSeparator]&quot;, GridBox[List[List[RowBox[List[TagBox[RowBox[List[&quot;-&quot;, FractionBox[&quot;k&quot;, &quot;4&quot;]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, &quot;k&quot;]], &quot;4&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[RowBox[List[&quot;2&quot;, &quot;-&quot;, &quot;k&quot;]], &quot;4&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[RowBox[List[&quot;3&quot;, &quot;-&quot;, &quot;k&quot;]], &quot;4&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[RowBox[List[RowBox[List[&quot;2&quot;, &quot;\[Nu]&quot;]], &quot;-&quot;, &quot;k&quot;]], &quot;4&quot;], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;4&quot;], &quot; 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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinKei", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["k", "4"]]], ",", FractionBox[RowBox[List["1", "-", "k"]], "4"], ",", FractionBox[RowBox[List["2", "-", "k"]], "4"], ",", FractionBox[RowBox[List["3", "-", "k"]], "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "-", "k"]], ")"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["\[Nu]", "+", "k", "-", "n"]], ")"]]]], ",", FractionBox[RowBox[List["\[Nu]", "-", "k"]], "4"], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["2", "-", "\[Nu]", "-", "k"]], ")"]]]], ",", RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], " ", RowBox[List["(", RowBox[List["\[Nu]", "+", "k"]], ")"]]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "-", "k"]], ")"]]]], ",", "0", ",", FractionBox["1", "4"], ",", FractionBox["1", "2"], ",", FractionBox["3", "4"]]], "}"]]]], "}"]], ",", FractionBox[SubscriptBox["zz", "0"], "4"], ",", FractionBox["1", "4"]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], ")"]], "k"]]], RowBox[List["k", "!"]]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Arg", "[", SubscriptBox["zz", "0"], "]"]], "]"]], "<", "\[Pi]"]]]]]]]]










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





2007-05-02