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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/11.06.06.0008.01









  


  










Input Form





MathieuCharacteristicB[7, q] \[Proportional] SeriesData[$CellContext`q, 0, {49, 0, Rational[1, 96], 0, Rational[7, 4423680], 0, Rational[17, 20384317440], Rational[-1, 2123366400], Rational[80617, 103324028239872000], Rational[1, 2174327193600], Rational[22381, 19044684885173207040], Rational[-121, 1502894956216320000], Rational[1585697167, 475355334733923247718400000], Rational[169, 4155203974946881536000], Rational[-4087866435403, 107331431740241997948832972800000], Rational[619, 11770607986095528345600000], Rational[127886416305104603, 2393782869301730012493396119126016000000], Rational[710653159, 5337927405856933273185288192000000], Rational[-4615810827596713259, 165458271926135578463543539753990225920000000], Rational[8903677513487, 13856405477219661667865298500321280000000], Rational[6648543660666518664511, 648066959480287833726007336508428916883456000000000]}, 0, 21, 1]










Standard Form





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MathML Form







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</mo> <msup> <mi> q </mi> <mn> 10 </mn> </msup> </mrow> <mn> 19044684885173207040 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 121 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 11 </mn> </msup> </mrow> <mn> 1502894956216320000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 1585697167 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 12 </mn> </msup> </mrow> <mn> 475355334733923247718400000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 169 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 13 </mn> </msup> </mrow> <mn> 4155203974946881536000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 4087866435403 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 14 </mn> </msup> </mrow> <mn> 107331431740241997948832972800000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 619 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 15 </mn> </msup> </mrow> <mn> 11770607986095528345600000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 127886416305104603 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 16 </mn> </msup> </mrow> <mn> 2393782869301730012493396119126016000000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 710653159 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 17 </mn> </msup> </mrow> <mn> 5337927405856933273185288192000000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 4615810827596713259 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 18 </mn> </msup> </mrow> <mn> 165458271926135578463543539753990225920000000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 8903677513487 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 19 </mn> </msup> </mrow> <mn> 13856405477219661667865298500321280000000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 6648543660666518664511 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 20 </mn> </msup> </mrow> <mn> 648066959480287833726007336508428916883456000000000 </mn> </mfrac> <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'> 49 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 96 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 7 <sep /> 4423680 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 17 <sep /> 20384317440 </cn> <cn type='rational'> -1 <sep /> 2123366400 </cn> <cn type='rational'> 80617 <sep /> 103324028239872000 </cn> <cn type='rational'> 1 <sep /> 2174327193600 </cn> <cn type='rational'> 22381 <sep /> 19044684885173207040 </cn> <cn type='rational'> -121 <sep /> 1502894956216320000 </cn> <cn type='rational'> 1585697167 <sep /> 475355334733923247718400000 </cn> <cn type='rational'> 169 <sep /> 4155203974946881536000 </cn> <cn type='rational'> -4087866435403 <sep /> 107331431740241997948832972800000 </cn> <cn type='rational'> 619 <sep /> 11770607986095528345600000 </cn> <cn type='rational'> 127886416305104603 <sep /> 2393782869301730012493396119126016000000 </cn> <cn type='rational'> 710653159 <sep /> 5337927405856933273185288192000000 </cn> <cn type='rational'> -4615810827596713259 <sep /> 165458271926135578463543539753990225920000000 </cn> <cn type='rational'> 8903677513487 <sep /> 13856405477219661667865298500321280000000 </cn> <cn type='rational'> 6648543660666518664511 <sep /> 648066959480287833726007336508428916883456000000000 </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'> 7 </cn> <ci> q </ci> </apply> <apply> <ci> SeriesData </ci> <ci> $CellContext`q </ci> <cn type='integer'> 0 </cn> <list> <cn type='integer'> 49 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 96 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 7 <sep /> 4423680 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 17 <sep /> 20384317440 </cn> <cn type='rational'> -1 <sep /> 2123366400 </cn> <cn type='rational'> 80617 <sep /> 103324028239872000 </cn> <cn type='rational'> 1 <sep /> 2174327193600 </cn> <cn type='rational'> 22381 <sep /> 19044684885173207040 </cn> <cn type='rational'> -121 <sep /> 1502894956216320000 </cn> <cn type='rational'> 1585697167 <sep /> 475355334733923247718400000 </cn> <cn type='rational'> 169 <sep /> 4155203974946881536000 </cn> <cn type='rational'> -4087866435403 <sep /> 107331431740241997948832972800000 </cn> <cn type='rational'> 619 <sep /> 11770607986095528345600000 </cn> <cn type='rational'> 127886416305104603 <sep /> 2393782869301730012493396119126016000000 </cn> <cn type='rational'> 710653159 <sep /> 5337927405856933273185288192000000 </cn> <cn type='rational'> -4615810827596713259 <sep /> 165458271926135578463543539753990225920000000 </cn> <cn type='rational'> 8903677513487 <sep /> 13856405477219661667865298500321280000000 </cn> <cn type='rational'> 6648543660666518664511 <sep /> 648066959480287833726007336508428916883456000000000 </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["7", ",", "q_"]], "]"]], "]"]], "\[RuleDelayed]", InterpretationBox[RowBox[List["49", "+", RowBox[List[FractionBox["1", "96"], " ", SuperscriptBox["$CellContext`q", "2"]]], "+", RowBox[List[FractionBox["7", "4423680"], " ", SuperscriptBox["$CellContext`q", "4"]]], "+", RowBox[List[FractionBox["17", "20384317440"], " ", SuperscriptBox["$CellContext`q", "6"]]], "-", RowBox[List[FractionBox["1", "2123366400"], " ", SuperscriptBox["$CellContext`q", "7"]]], "+", RowBox[List[FractionBox["80617", "103324028239872000"], " ", SuperscriptBox["$CellContext`q", "8"]]], "+", RowBox[List[FractionBox["1", "2174327193600"], " ", SuperscriptBox["$CellContext`q", "9"]]], "+", RowBox[List[FractionBox["22381", "19044684885173207040"], " ", SuperscriptBox["$CellContext`q", "10"]]], "-", RowBox[List[FractionBox["121", "1502894956216320000"], " ", SuperscriptBox["$CellContext`q", "11"]]], "+", RowBox[List[FractionBox["1585697167", "475355334733923247718400000"], " ", SuperscriptBox["$CellContext`q", "12"]]], "+", RowBox[List[FractionBox["169", "4155203974946881536000"], " ", SuperscriptBox["$CellContext`q", "13"]]], "-", RowBox[List[FractionBox["4087866435403", "107331431740241997948832972800000"], " ", SuperscriptBox["$CellContext`q", "14"]]], "+", RowBox[List[FractionBox["619", "11770607986095528345600000"], " ", SuperscriptBox["$CellContext`q", "15"]]], "+", RowBox[List[FractionBox["127886416305104603", "2393782869301730012493396119126016000000"], " ", SuperscriptBox["$CellContext`q", "16"]]], "+", RowBox[List[FractionBox["710653159", "5337927405856933273185288192000000"], " ", SuperscriptBox["$CellContext`q", "17"]]], "-", RowBox[List[FractionBox["4615810827596713259", "165458271926135578463543539753990225920000000"], " ", SuperscriptBox["$CellContext`q", "18"]]], "+", RowBox[List[FractionBox["8903677513487", "13856405477219661667865298500321280000000"], " ", SuperscriptBox["$CellContext`q", "19"]]], "+", RowBox[List[FractionBox["6648543660666518664511", "648066959480287833726007336508428916883456000000000"], " ", 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[49, 0, Rational[1, 96], 0, Rational[7, 4423680], 0, Rational[17, 20384317440], Rational[-1, 2123366400], Rational[80617, 103324028239872000], Rational[1, 2174327193600], Rational[22381, 19044684885173207040], Rational[-121, 1502894956216320000], Rational[1585697167, 475355334733923247718400000], Rational[169, 4155203974946881536000], Rational[-4087866435403, 107331431740241997948832972800000], Rational[619, 11770607986095528345600000], Rational[127886416305104603, 2393782869301730012493396119126016000000], Rational[710653159, 5337927405856933273185288192000000], Rational[-4615810827596713259, 165458271926135578463543539753990225920000000], Rational[8903677513487, 13856405477219661667865298500321280000000], Rational[6648543660666518664511, 648066959480287833726007336508428916883456000000000]], 0, 21, 1], Rule[Editable, False]]]]]]










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





2001-10-29





© 1998- Wolfram Research, Inc.