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variants of this functions
KelvinBei






Mathematica Notation

Traditional Notation









Bessel-Type Functions > KelvinBei[z] > Series representations > Generalized power series > Expansions at z==0 > For small integer powers of the function





http://functions.wolfram.com/03.13.06.0013.01









  


  










Input Form





KelvinBei[z]^2 \[Proportional] (z^4/16) (1 - z^4/288 + (59 z^8)/16588800 - z^12/1040449536 + O[z^16]) /; (z -> 0)










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["KelvinBei", "[", "z", "]"]], "2"], "\[Proportional]", RowBox[List[FractionBox[SuperscriptBox["z", "4"], "16"], " ", RowBox[List["(", RowBox[List["1", "-", FractionBox[SuperscriptBox["z", "4"], "288"], "+", FractionBox[RowBox[List["59", " ", SuperscriptBox["z", "8"]]], "16588800"], "-", FractionBox[SuperscriptBox["z", "12"], "1040449536"], "+", RowBox[List["O", "[", SuperscriptBox["z", "16"], "]"]]]], ")"]]]]]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", "0"]], ")"]]]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mrow> <mi> bei </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8733; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 16 </mn> </mfrac> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <msup> <mi> z </mi> <mn> 4 </mn> </msup> <mn> 288 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 59 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mn> 16588800 </mn> </mfrac> <mo> - </mo> <mfrac> <msup> <mi> z </mi> <mn> 12 </mn> </msup> <mn> 1040449536 </mn> </mfrac> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <msup> <mi> z </mi> <mn> 16 </mn> </msup> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <power /> <apply> <ci> KelvinBei </ci> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 16 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <cn type='integer'> 288 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 59 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> <apply> <power /> <cn type='integer'> 16588800 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 12 </cn> </apply> <apply> <power /> <cn type='integer'> 1040449536 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> O </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 16 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <ci> Rule </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["KelvinBei", "[", "z_", "]"]], "2"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "16"], " ", SuperscriptBox["z", "4"], " ", RowBox[List["(", RowBox[List["1", "-", FractionBox[SuperscriptBox["z", "4"], "288"], "+", FractionBox[RowBox[List["59", " ", SuperscriptBox["z", "8"]]], "16588800"], "-", FractionBox[SuperscriptBox["z", "12"], "1040449536"], "+", SuperscriptBox[RowBox[List["O", "[", "z", "]"]], "16"]]], ")"]]]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", "0"]], ")"]]]]]]]]










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





2007-05-02