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MathieuCharacteristicB






Mathematica Notation

Traditional Notation









Mathieu and Spheroidal Functions > MathieuCharacteristicB[r,q] > Series representations > Generalized power series > Expansions at q==0





http://functions.wolfram.com/11.06.06.0011.01









  


  










Input Form





MathieuCharacteristicB[10, q] \[Proportional] SeriesData[$CellContext`q, 0, {100, 0, Rational[1, 198], 0, Rational[169, 993586176], 0, Rational[31943, 1772341136197632], 0, Rational[1704670559, 569203604713406176690176], 0, Rational[-1768418729052839, 62482162733716252102692647731200], 0, Rational[1119707449608181806019, 123640255459938983842746782311963321958400], 0, Rational[-24606893441988925522607, 34245100789973865842579849356421640003728179200], 0, Rational[270635998049518041370843201, 3368176723821395783072385039067573491742813047320739840], 0, Rational[11314282409772177042594165212832017, 356159753797099085314066801692056277942540168039466400750134886400], 0, Rational[-47256590145830056043660165066696641992589, 446812383611567121300\ 885596593131978254699031930215704800265218765619200000]}, 0, 21, 1]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["MathieuCharacteristicB", "[", RowBox[List["10", ",", "q"]], "]"]], "\[Proportional]", InterpretationBox[RowBox[List["100", "+", FractionBox[SuperscriptBox["q", "2"], "198"], "+", FractionBox[RowBox[List["169", " ", SuperscriptBox["q", "4"]]], "993586176"], "+", FractionBox[RowBox[List["31943", " ", SuperscriptBox["q", "6"]]], "1772341136197632"], "+", FractionBox[RowBox[List["1704670559", " ", SuperscriptBox["q", "8"]]], "569203604713406176690176"], "-", FractionBox[RowBox[List["1768418729052839", " ", SuperscriptBox["q", "10"]]], "62482162733716252102692647731200"], "+", FractionBox[RowBox[List["1119707449608181806019", " ", SuperscriptBox["q", "12"]]], "123640255459938983842746782311963321958400"], "-", FractionBox[RowBox[List["24606893441988925522607", " ", SuperscriptBox["q", "14"]]], "34245100789973865842579849356421640003728179200"], "+", FractionBox[RowBox[List["270635998049518041370843201", " ", SuperscriptBox["q", "16"]]], "3368176723821395783072385039067573491742813047320739840"], "+", FractionBox[RowBox[List["11314282409772177042594165212832017", " ", SuperscriptBox["q", "18"]]], "356159753797099085314066801692056277942540168039466400750134886400"], "-", RowBox[List[RowBox[List["(", RowBox[List["47256590145830056043660165066696641992589", " ", SuperscriptBox["q", "20"]]], ")"]], "/", "446812383611567121300885596593131978254699031930215704800265218765619200000"]], "+", InterpretationBox[SuperscriptBox[RowBox[List["O", "[", "q", "]"]], "21"], SeriesData[$CellContext`q, 0, List[], 0, 21, 1]]]], SeriesData[$CellContext`q, 0, List[100, 0, Rational[1, 198], 0, Rational[169, 993586176], 0, Rational[31943, 1772341136197632], 0, Rational[1704670559, 569203604713406176690176], 0, Rational[-1768418729052839, 62482162733716252102692647731200], 0, Rational[1119707449608181806019, 123640255459938983842746782311963321958400], 0, Rational[-24606893441988925522607, 34245100789973865842579849356421640003728179200], 0, Rational[270635998049518041370843201, 3368176723821395783072385039067573491742813047320739840], 0, Rational[11314282409772177042594165212832017, 356159753797099085314066801692056277942540168039466400750134886400], 0, Rational[-47256590145830056043660165066696641992589, 446812383611567121300885596593131978254699031930215704800265218765619200000]], 0, 21, 1]]]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <semantics> <mi> b </mi> <annotation-xml encoding='MathML-Content'> <ci> MathieuCharacteristicB </ci> </annotation-xml> </semantics> <mn> 10 </mn> </msub> <mo> ( </mo> <mi> q </mi> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <semantics> <mrow> <mn> 100 </mn> <mo> + </mo> <mfrac> <msup> <mi> q </mi> <mn> 2 </mn> </msup> <mn> 198 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 169 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 4 </mn> </msup> </mrow> <mn> 993586176 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 31943 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 6 </mn> </msup> </mrow> <mn> 1772341136197632 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 1704670559 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 8 </mn> </msup> </mrow> <mn> 569203604713406176690176 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 1768418729052839 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 10 </mn> </msup> </mrow> <mn> 62482162733716252102692647731200 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 1119707449608181806019 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 12 </mn> </msup> </mrow> <mn> 123640255459938983842746782311963321958400 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 24606893441988925522607 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 14 </mn> </msup> </mrow> <mn> 34245100789973865842579849356421640003728179200 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 270635998049518041370843201 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 16 </mn> </msup> </mrow> <mn> 3368176723821395783072385039067573491742813047320739840 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 11314282409772177042594165212832017 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 18 </mn> </msup> </mrow> <mn> 356159753797099085314066801692056277942540168039466400750134886400 </mn> </mfrac> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 47256590145830056043660165066696641992589 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 20 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mn> 446812383611567121300885596593131978254699031930215704800265218765619200000 </mn> </mrow> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <msup> <mi> q </mi> <mn> 21 </mn> </msup> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> SeriesData </ci> <ci> $CellContext`q </ci> <cn type='integer'> 0 </cn> <list> <cn type='integer'> 100 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 198 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 169 <sep /> 993586176 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 31943 <sep /> 1772341136197632 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1704670559 <sep /> 569203604713406176690176 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -1768418729052839 <sep /> 62482162733716252102692647731200 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1119707449608181806019 <sep /> 123640255459938983842746782311963321958400 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -24606893441988925522607 <sep /> 34245100789973865842579849356421640003728179200 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 270635998049518041370843201 <sep /> 3368176723821395783072385039067573491742813047320739840 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 11314282409772177042594165212832017 <sep /> 356159753797099085314066801692056277942540168039466400750134886400 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -47256590145830056043660165066696641992589 <sep /> 446812383611567121300885596593131978254699031930215704800265218765619200000 </cn> </list> <cn type='integer'> 0 </cn> <cn type='integer'> 21 </cn> <cn type='integer'> 1 </cn> </apply> </annotation-xml> </semantics> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportional </ci> <apply> <ci> MathieuCharacteristicB </ci> <cn type='integer'> 10 </cn> <ci> q </ci> </apply> <apply> <ci> SeriesData </ci> <ci> $CellContext`q </ci> <cn type='integer'> 0 </cn> <list> <cn type='integer'> 100 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 198 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 169 <sep /> 993586176 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 31943 <sep /> 1772341136197632 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1704670559 <sep /> 569203604713406176690176 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -1768418729052839 <sep /> 62482162733716252102692647731200 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1119707449608181806019 <sep /> 123640255459938983842746782311963321958400 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -24606893441988925522607 <sep /> 34245100789973865842579849356421640003728179200 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 270635998049518041370843201 <sep /> 3368176723821395783072385039067573491742813047320739840 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 11314282409772177042594165212832017 <sep /> 356159753797099085314066801692056277942540168039466400750134886400 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -47256590145830056043660165066696641992589 <sep /> 446812383611567121300885596593131978254699031930215704800265218765619200000 </cn> </list> <cn type='integer'> 0 </cn> <cn type='integer'> 21 </cn> <cn type='integer'> 1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["MathieuCharacteristicB", "[", RowBox[List["10", ",", "q_"]], "]"]], "]"]], "\[RuleDelayed]", InterpretationBox[RowBox[List["100", "+", RowBox[List[FractionBox["1", "198"], " ", SuperscriptBox["$CellContext`q", "2"]]], "+", RowBox[List[FractionBox["169", "993586176"], " ", SuperscriptBox["$CellContext`q", "4"]]], "+", RowBox[List[FractionBox["31943", "1772341136197632"], " ", SuperscriptBox["$CellContext`q", "6"]]], "+", RowBox[List[FractionBox["1704670559", "569203604713406176690176"], " ", SuperscriptBox["$CellContext`q", "8"]]], "-", RowBox[List[FractionBox["1768418729052839", "62482162733716252102692647731200"], " ", SuperscriptBox["$CellContext`q", "10"]]], "+", RowBox[List[FractionBox["1119707449608181806019", "123640255459938983842746782311963321958400"], " ", SuperscriptBox["$CellContext`q", "12"]]], "-", RowBox[List[FractionBox["24606893441988925522607", "34245100789973865842579849356421640003728179200"], " ", SuperscriptBox["$CellContext`q", "14"]]], "+", RowBox[List[FractionBox["270635998049518041370843201", "3368176723821395783072385039067573491742813047320739840"], " ", SuperscriptBox["$CellContext`q", "16"]]], "+", RowBox[List[FractionBox["11314282409772177042594165212832017", "356159753797099085314066801692056277942540168039466400750134886400"], " ", SuperscriptBox["$CellContext`q", "18"]]], "-", RowBox[List[FractionBox["47256590145830056043660165066696641992589", "446812383611567121300885596593131978254699031930215704800265218765619200000"], " ", SuperscriptBox["$CellContext`q", "20"]]], "+", InterpretationBox[SuperscriptBox[RowBox[List["O", "[", "$CellContext`q", "]"]], "21"], SeriesData[$CellContext`q, 0, List[], 0, 21, 1], Rule[Editable, False]]]], SeriesData[$CellContext`q, 0, List[100, 0, Rational[1, 198], 0, Rational[169, 993586176], 0, Rational[31943, 1772341136197632], 0, Rational[1704670559, 569203604713406176690176], 0, Rational[-1768418729052839, 62482162733716252102692647731200], 0, Rational[1119707449608181806019, 123640255459938983842746782311963321958400], 0, Rational[-24606893441988925522607, 34245100789973865842579849356421640003728179200], 0, Rational[270635998049518041370843201, 3368176723821395783072385039067573491742813047320739840], 0, Rational[11314282409772177042594165212832017, 356159753797099085314066801692056277942540168039466400750134886400], 0, Rational[-47256590145830056043660165066696641992589, 446812383611567121300885596593131978254699031930215704800265218765619200000]], 0, 21, 1], Rule[Editable, False]]]]]]










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





2001-10-29





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