MathieuCharacteristicA[3, q] \[Proportional] SeriesData[$CellContext`q, 0, {9, 0, Rational[1, 16], Rational[1, 64], Rational[13, 20480], Rational[-5, 16384], Rational[-1961, 23592960], Rational[-609, 104857600], Rational[4957199, 2113929216000], Rational[872713, 1087163596800], Rational[421511, 6012954214400], Rational[-16738435813, 681869007912960000], Rational[-572669780189, 60115798248652800000], Rational[-27992567161, 29093077670952960000], Rational[110350873865291, 377046286615550361600000], Rational[10234605999596669, 81441997908958878105600000], Rational[704720978382089561, 49548909345104858185728000000], Rational[-195640795481512957, 52122878661733681987584000000], Rational[-40878632822977874980039, 23117539144052122635133255680000000], Rational[-38723118606468500148773, 175807458181927253620272660480000000], Rational[96836518225571706158506019, 1923379256785136603243086872576000000000]}, 0, 21, 1]

Cell[BoxData[RowBox[List[RowBox[List["MathieuCharacteristicA", "[", RowBox[List["3", ",", "q"]], "]"]], "\[Proportional]", InterpretationBox[RowBox[List["9", "+", FractionBox[SuperscriptBox["q", "2"], "16"], "+", FractionBox[SuperscriptBox["q", "3"], "64"], "+", FractionBox[RowBox[List["13", " ", SuperscriptBox["q", "4"]]], "20480"], "-", FractionBox[RowBox[List["5", " ", SuperscriptBox["q", "5"]]], "16384"], "-", FractionBox[RowBox[List["1961", " ", SuperscriptBox["q", "6"]]], "23592960"], "-", FractionBox[RowBox[List["609", " ", SuperscriptBox["q", "7"]]], "104857600"], "+", FractionBox[RowBox[List["4957199", " ", SuperscriptBox["q", "8"]]], "2113929216000"], "+", FractionBox[RowBox[List["872713", " ", SuperscriptBox["q", "9"]]], "1087163596800"], "+", FractionBox[RowBox[List["421511", " ", SuperscriptBox["q", "10"]]], "6012954214400"], "-", FractionBox[RowBox[List["16738435813", " ", SuperscriptBox["q", "11"]]], "681869007912960000"], "-", FractionBox[RowBox[List["572669780189", " ", SuperscriptBox["q", "12"]]], "60115798248652800000"], "-", FractionBox[RowBox[List["27992567161", " ", SuperscriptBox["q", "13"]]], "29093077670952960000"], "+", FractionBox[RowBox[List["110350873865291", " ", SuperscriptBox["q", "14"]]], "377046286615550361600000"], "+", FractionBox[RowBox[List["10234605999596669", " ", SuperscriptBox["q", "15"]]], "81441997908958878105600000"], "+", FractionBox[RowBox[List["704720978382089561", " ", SuperscriptBox["q", "16"]]], "49548909345104858185728000000"], "-", FractionBox[RowBox[List["195640795481512957", " ", SuperscriptBox["q", "17"]]], "52122878661733681987584000000"], "-", FractionBox[RowBox[List["40878632822977874980039", " ", SuperscriptBox["q", "18"]]], "23117539144052122635133255680000000"], "-", FractionBox[RowBox[List["38723118606468500148773", " ", SuperscriptBox["q", "19"]]], "175807458181927253620272660480000000"], "+", FractionBox[RowBox[List["96836518225571706158506019", " ", SuperscriptBox["q", "20"]]], "1923379256785136603243086872576000000000"], "+", InterpretationBox[SuperscriptBox[RowBox[List["O", "[", "q", "]"]], "21"], SeriesData[$CellContext`q, 0, List[], 0, 21, 1]]]], SeriesData[$CellContext`q, 0, List[9, 0, Rational[1, 16], Rational[1, 64], Rational[13, 20480], Rational[-5, 16384], Rational[-1961, 23592960], Rational[-609, 104857600], Rational[4957199, 2113929216000], Rational[872713, 1087163596800], Rational[421511, 6012954214400], Rational[-16738435813, 681869007912960000], Rational[-572669780189, 60115798248652800000], Rational[-27992567161, 29093077670952960000], Rational[110350873865291, 377046286615550361600000], Rational[10234605999596669, 81441997908958878105600000], Rational[704720978382089561, 49548909345104858185728000000], Rational[-195640795481512957, 52122878661733681987584000000], Rational[-40878632822977874980039, 23117539144052122635133255680000000], Rational[-38723118606468500148773, 175807458181927253620272660480000000], Rational[96836518225571706158506019, 1923379256785136603243086872576000000000]], 0, 21, 1]]]]]]

<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> a </mi> <annotation-xml encoding='MathML-Content'> <ci> MathieuCharacteristicA </ci> </annotation-xml> </semantics> <mn> 3 </mn> </msub> <mo> ( </mo> <mi> q </mi> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <semantics> <mrow> <mn> 9 </mn> <mo> + </mo> <mfrac> <msup> <mi> q </mi> <mn> 2 </mn> </msup> <mn> 16 </mn> </mfrac> <mo> + </mo> <mfrac> <msup> <mi> q </mi> <mn> 3 </mn> </msup> <mn> 64 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 13 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 4 </mn> </msup> </mrow> <mn> 20480 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 5 </mn> </msup> </mrow> <mn> 16384 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 1961 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 6 </mn> </msup> </mrow> <mn> 23592960 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 609 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 7 </mn> </msup> </mrow> <mn> 104857600 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 4957199 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 8 </mn> </msup> </mrow> <mn> 2113929216000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 872713 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 9 </mn> </msup> </mrow> <mn> 1087163596800 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 421511 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 10 </mn> </msup> </mrow> <mn> 6012954214400 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 16738435813 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 11 </mn> </msup> </mrow> <mn> 681869007912960000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 572669780189 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 12 </mn> </msup> </mrow> <mn> 60115798248652800000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 27992567161 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 13 </mn> </msup> </mrow> <mn> 29093077670952960000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 110350873865291 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 14 </mn> </msup> </mrow> <mn> 377046286615550361600000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 10234605999596669 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 15 </mn> </msup> </mrow> <mn> 81441997908958878105600000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 704720978382089561 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 16 </mn> </msup> </mrow> <mn> 49548909345104858185728000000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 195640795481512957 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 17 </mn> </msup> </mrow> <mn> 52122878661733681987584000000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 40878632822977874980039 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 18 </mn> </msup> </mrow> <mn> 23117539144052122635133255680000000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 38723118606468500148773 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 19 </mn> </msup> </mrow> <mn> 175807458181927253620272660480000000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 96836518225571706158506019 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 20 </mn> </msup> </mrow> <mn> 1923379256785136603243086872576000000000 </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'> 9 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 16 </cn> <cn type='rational'> 1 <sep /> 64 </cn> <cn type='rational'> 13 <sep /> 20480 </cn> <cn type='rational'> -5 <sep /> 16384 </cn> <cn type='rational'> -1961 <sep /> 23592960 </cn> <cn type='rational'> -609 <sep /> 104857600 </cn> <cn type='rational'> 4957199 <sep /> 2113929216000 </cn> <cn type='rational'> 872713 <sep /> 1087163596800 </cn> <cn type='rational'> 421511 <sep /> 6012954214400 </cn> <cn type='rational'> -16738435813 <sep /> 681869007912960000 </cn> <cn type='rational'> -572669780189 <sep /> 60115798248652800000 </cn> <cn type='rational'> -27992567161 <sep /> 29093077670952960000 </cn> <cn type='rational'> 110350873865291 <sep /> 377046286615550361600000 </cn> <cn type='rational'> 10234605999596669 <sep /> 81441997908958878105600000 </cn> <cn type='rational'> 704720978382089561 <sep /> 49548909345104858185728000000 </cn> <cn type='rational'> -195640795481512957 <sep /> 52122878661733681987584000000 </cn> <cn type='rational'> -40878632822977874980039 <sep /> 23117539144052122635133255680000000 </cn> <cn type='rational'> -38723118606468500148773 <sep /> 175807458181927253620272660480000000 </cn> <cn type='rational'> 96836518225571706158506019 <sep /> 1923379256785136603243086872576000000000 </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> MathieuCharacteristicA </ci> <cn type='integer'> 3 </cn> <ci> q </ci> </apply> <apply> <ci> SeriesData </ci> <ci> $CellContext`q </ci> <cn type='integer'> 0 </cn> <list> <cn type='integer'> 9 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 16 </cn> <cn type='rational'> 1 <sep /> 64 </cn> <cn type='rational'> 13 <sep /> 20480 </cn> <cn type='rational'> -5 <sep /> 16384 </cn> <cn type='rational'> -1961 <sep /> 23592960 </cn> <cn type='rational'> -609 <sep /> 104857600 </cn> <cn type='rational'> 4957199 <sep /> 2113929216000 </cn> <cn type='rational'> 872713 <sep /> 1087163596800 </cn> <cn type='rational'> 421511 <sep /> 6012954214400 </cn> <cn type='rational'> -16738435813 <sep /> 681869007912960000 </cn> <cn type='rational'> -572669780189 <sep /> 60115798248652800000 </cn> <cn type='rational'> -27992567161 <sep /> 29093077670952960000 </cn> <cn type='rational'> 110350873865291 <sep /> 377046286615550361600000 </cn> <cn type='rational'> 10234605999596669 <sep /> 81441997908958878105600000 </cn> <cn type='rational'> 704720978382089561 <sep /> 49548909345104858185728000000 </cn> <cn type='rational'> -195640795481512957 <sep /> 52122878661733681987584000000 </cn> <cn type='rational'> -40878632822977874980039 <sep /> 23117539144052122635133255680000000 </cn> <cn type='rational'> -38723118606468500148773 <sep /> 175807458181927253620272660480000000 </cn> <cn type='rational'> 96836518225571706158506019 <sep /> 1923379256785136603243086872576000000000 </cn> </list> <cn type='integer'> 0 </cn> <cn type='integer'> 21 </cn> <cn type='integer'> 1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["MathieuCharacteristicA", "[", RowBox[List["3", ",", "q_"]], "]"]], "]"]], "\[RuleDelayed]", InterpretationBox[RowBox[List["9", "+", RowBox[List[FractionBox["1", "16"], " ", SuperscriptBox["$CellContext`q", "2"]]], "+", RowBox[List[FractionBox["1", "64"], " ", SuperscriptBox["$CellContext`q", "3"]]], "+", RowBox[List[FractionBox["13", "20480"], " ", SuperscriptBox["$CellContext`q", "4"]]], "-", RowBox[List[FractionBox["5", "16384"], " ", SuperscriptBox["$CellContext`q", "5"]]], "-", RowBox[List[FractionBox["1961", "23592960"], " ", SuperscriptBox["$CellContext`q", "6"]]], "-", RowBox[List[FractionBox["609", "104857600"], " ", SuperscriptBox["$CellContext`q", "7"]]], "+", RowBox[List[FractionBox["4957199", "2113929216000"], " ", SuperscriptBox["$CellContext`q", "8"]]], "+", RowBox[List[FractionBox["872713", "1087163596800"], " ", SuperscriptBox["$CellContext`q", "9"]]], "+", RowBox[List[FractionBox["421511", "6012954214400"], " ", SuperscriptBox["$CellContext`q", "10"]]], "-", RowBox[List[FractionBox["16738435813", "681869007912960000"], " ", SuperscriptBox["$CellContext`q", "11"]]], "-", RowBox[List[FractionBox["572669780189", "60115798248652800000"], " ", SuperscriptBox["$CellContext`q", "12"]]], "-", RowBox[List[FractionBox["27992567161", "29093077670952960000"], " ", SuperscriptBox["$CellContext`q", "13"]]], "+", RowBox[List[FractionBox["110350873865291", "377046286615550361600000"], " ", SuperscriptBox["$CellContext`q", "14"]]], "+", RowBox[List[FractionBox["10234605999596669", "81441997908958878105600000"], " ", SuperscriptBox["$CellContext`q", "15"]]], "+", RowBox[List[FractionBox["704720978382089561", "49548909345104858185728000000"], " ", SuperscriptBox["$CellContext`q", "16"]]], "-", RowBox[List[FractionBox["195640795481512957", "52122878661733681987584000000"], " ", SuperscriptBox["$CellContext`q", "17"]]], "-", RowBox[List[FractionBox["40878632822977874980039", "23117539144052122635133255680000000"], " ", SuperscriptBox["$CellContext`q", "18"]]], "-", RowBox[List[FractionBox["38723118606468500148773", "175807458181927253620272660480000000"], " ", SuperscriptBox["$CellContext`q", "19"]]], "+", RowBox[List[FractionBox["96836518225571706158506019", "1923379256785136603243086872576000000000"], " ", 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[9, 0, Rational[1, 16], Rational[1, 64], Rational[13, 20480], Rational[-5, 16384], Rational[-1961, 23592960], Rational[-609, 104857600], Rational[4957199, 2113929216000], Rational[872713, 1087163596800], Rational[421511, 6012954214400], Rational[-16738435813, 681869007912960000], Rational[-572669780189, 60115798248652800000], Rational[-27992567161, 29093077670952960000], Rational[110350873865291, 377046286615550361600000], Rational[10234605999596669, 81441997908958878105600000], Rational[704720978382089561, 49548909345104858185728000000], Rational[-195640795481512957, 52122878661733681987584000000], Rational[-40878632822977874980039, 23117539144052122635133255680000000], Rational[-38723118606468500148773, 175807458181927253620272660480000000], Rational[96836518225571706158506019, 1923379256785136603243086872576000000000]], 0, 21, 1], Rule[Editable, False]]]]]]

2001-10-29