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variants of this functions
KelvinBei






Mathematica Notation

Traditional Notation









Bessel-Type Functions > KelvinBei[nu,z] > Series representations > Generalized power series > Expansions at z==0 > For the function itself > General case





http://functions.wolfram.com/03.17.06.0014.01









  


  










Input Form





KelvinBei[\[Nu], z] \[Proportional] ((z^\[Nu] Sin[(3 Pi \[Nu])/4])/(2^\[Nu] Gamma[1 + \[Nu]])) (1 - z^4/(32 (1 + \[Nu]) (2 + \[Nu])) + z^8/(6144 (1 + \[Nu]) (2 + \[Nu]) (3 + \[Nu]) (4 + \[Nu])) + \[Ellipsis]) + ((2^(-2 - \[Nu]) z^(2 + \[Nu]) Cos[(3 Pi \[Nu])/4])/ Gamma[2 + \[Nu]]) (1 - z^4/(96 (2 + \[Nu]) (3 + \[Nu])) + z^8/(30720 (2 + \[Nu]) (3 + \[Nu]) (4 + \[Nu]) (5 + \[Nu])) + \[Ellipsis]) /; (z -> 0) && !(Element[-\[Nu], Integers] && -\[Nu] > 0)










Standard Form





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MathML Form







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</ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 30720 </cn> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 4 </cn> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> &#8230; </ci> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <ci> Rule </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> <apply> <notin /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinBei", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List["-", "\[Nu]"]]], " ", SuperscriptBox["z", "\[Nu]"], " ", RowBox[List["Sin", "[", FractionBox[RowBox[List["3", " ", "\[Pi]", " ", "\[Nu]"]], "4"], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", FractionBox[SuperscriptBox["z", "4"], RowBox[List["32", " ", RowBox[List["(", RowBox[List["1", "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", "\[Nu]"]], ")"]]]]], "+", FractionBox[SuperscriptBox["z", "8"], RowBox[List["6144", " ", RowBox[List["(", RowBox[List["1", "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List["3", "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List["4", "+", "\[Nu]"]], ")"]]]]], "+", "\[Ellipsis]"]], ")"]]]], RowBox[List["Gamma", "[", RowBox[List["1", "+", "\[Nu]"]], "]"]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", "\[Nu]"]]], " ", SuperscriptBox["z", RowBox[List["2", "+", "\[Nu]"]]], " ", RowBox[List["Cos", "[", FractionBox[RowBox[List["3", " ", "\[Pi]", " ", "\[Nu]"]], "4"], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", FractionBox[SuperscriptBox["z", "4"], RowBox[List["96", " ", RowBox[List["(", RowBox[List["2", "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List["3", "+", "\[Nu]"]], ")"]]]]], "+", FractionBox[SuperscriptBox["z", "8"], RowBox[List["30720", " ", RowBox[List["(", RowBox[List["2", "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List["3", "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List["4", "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List["5", "+", "\[Nu]"]], ")"]]]]], "+", "\[Ellipsis]"]], ")"]]]], RowBox[List["Gamma", "[", RowBox[List["2", "+", "\[Nu]"]], "]"]]]]], "/;", RowBox[List[RowBox[List["(", RowBox[List["z", "\[Rule]", "0"]], ")"]], "&&", RowBox[List["!", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[Nu]"]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["-", "\[Nu]"]], ">", "0"]]]], ")"]]]]]]]]]]]]










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





2007-05-02





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