Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site ContributeEmail CommentsSign the Guestbook

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











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/11.06.06.0002.01









  


  










Input Form





MathieuCharacteristicB[1, q] \[Proportional] SeriesData[$CellContext`q, 0, {1, -1, Rational[-1, 8], Rational[1, 64], Rational[-1, 1536], Rational[-11, 36864], Rational[49, 589824], Rational[-55, 9437184], Rational[-83, 35389440], Rational[12121, 15099494400], Rational[-114299, 1630745395200], Rational[-192151, 7827577896960], Rational[83513957, 8766887244595200], Rational[-944750239, 981891371394662400], Rational[-27587714461, 94261571653887590400], Rational[45487147753, 361964435150928347136], Rational[-11583279236477, 814419979089588781056000], Rational[-4401918060178787, 1172764769889007844720640000], Rational[20737942737397933, 11727647698890078447206400000], Rational[-206649295526133419, 938211815911206275776512000000], Rational[-230932630430735533, 4586813322232564014907392000000]}, 0, 21, 1]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["MathieuCharacteristicB", "[", RowBox[List["1", ",", "q"]], "]"]], "\[Proportional]", InterpretationBox[RowBox[List["1", "-", "q", "-", FractionBox[SuperscriptBox["q", "2"], "8"], "+", FractionBox[SuperscriptBox["q", "3"], "64"], "-", FractionBox[SuperscriptBox["q", "4"], "1536"], "-", FractionBox[RowBox[List["11", " ", SuperscriptBox["q", "5"]]], "36864"], "+", FractionBox[RowBox[List["49", " ", SuperscriptBox["q", "6"]]], "589824"], "-", FractionBox[RowBox[List["55", " ", SuperscriptBox["q", "7"]]], "9437184"], "-", FractionBox[RowBox[List["83", " ", SuperscriptBox["q", "8"]]], "35389440"], "+", FractionBox[RowBox[List["12121", " ", SuperscriptBox["q", "9"]]], "15099494400"], "-", FractionBox[RowBox[List["114299", " ", SuperscriptBox["q", "10"]]], "1630745395200"], "-", FractionBox[RowBox[List["192151", " ", SuperscriptBox["q", "11"]]], "7827577896960"], "+", FractionBox[RowBox[List["83513957", " ", SuperscriptBox["q", "12"]]], "8766887244595200"], "-", FractionBox[RowBox[List["944750239", " ", SuperscriptBox["q", "13"]]], "981891371394662400"], "-", FractionBox[RowBox[List["27587714461", " ", SuperscriptBox["q", "14"]]], "94261571653887590400"], "+", FractionBox[RowBox[List["45487147753", " ", SuperscriptBox["q", "15"]]], "361964435150928347136"], "-", FractionBox[RowBox[List["11583279236477", " ", SuperscriptBox["q", "16"]]], "814419979089588781056000"], "-", FractionBox[RowBox[List["4401918060178787", " ", SuperscriptBox["q", "17"]]], "1172764769889007844720640000"], "+", FractionBox[RowBox[List["20737942737397933", " ", SuperscriptBox["q", "18"]]], "11727647698890078447206400000"], "-", FractionBox[RowBox[List["206649295526133419", " ", SuperscriptBox["q", "19"]]], "938211815911206275776512000000"], "-", FractionBox[RowBox[List["230932630430735533", " ", SuperscriptBox["q", "20"]]], "4586813322232564014907392000000"], "+", InterpretationBox[SuperscriptBox[RowBox[List["O", "[", "q", "]"]], "21"], SeriesData[$CellContext`q, 0, List[], 0, 21, 1]]]], SeriesData[$CellContext`q, 0, List[1, -1, Rational[-1, 8], Rational[1, 64], Rational[-1, 1536], Rational[-11, 36864], Rational[49, 589824], Rational[-55, 9437184], Rational[-83, 35389440], Rational[12121, 15099494400], Rational[-114299, 1630745395200], Rational[-192151, 7827577896960], Rational[83513957, 8766887244595200], Rational[-944750239, 981891371394662400], Rational[-27587714461, 94261571653887590400], Rational[45487147753, 361964435150928347136], Rational[-11583279236477, 814419979089588781056000], Rational[-4401918060178787, 1172764769889007844720640000], Rational[20737942737397933, 11727647698890078447206400000], Rational[-206649295526133419, 938211815911206275776512000000], Rational[-230932630430735533, 4586813322232564014907392000000]], 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> 1 </mn> </msub> <mo> ( </mo> <mi> q </mi> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <semantics> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> q </mi> <mo> - </mo> <mfrac> <msup> <mi> q </mi> <mn> 2 </mn> </msup> <mn> 8 </mn> </mfrac> <mo> + </mo> <mfrac> <msup> <mi> q </mi> <mn> 3 </mn> </msup> <mn> 64 </mn> </mfrac> <mo> - </mo> <mfrac> <msup> <mi> q </mi> <mn> 4 </mn> </msup> <mn> 1536 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 11 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 5 </mn> </msup> </mrow> <mn> 36864 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 49 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 6 </mn> </msup> </mrow> <mn> 589824 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 55 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 7 </mn> </msup> </mrow> <mn> 9437184 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 83 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 8 </mn> </msup> </mrow> <mn> 35389440 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 12121 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 9 </mn> </msup> </mrow> <mn> 15099494400 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 114299 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 10 </mn> </msup> </mrow> <mn> 1630745395200 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 192151 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 11 </mn> </msup> </mrow> <mn> 7827577896960 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 83513957 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 12 </mn> </msup> </mrow> <mn> 8766887244595200 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 944750239 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 13 </mn> </msup> </mrow> <mn> 981891371394662400 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 27587714461 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 14 </mn> </msup> </mrow> <mn> 94261571653887590400 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 45487147753 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 15 </mn> </msup> </mrow> <mn> 361964435150928347136 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 11583279236477 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 16 </mn> </msup> </mrow> <mn> 814419979089588781056000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 4401918060178787 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 17 </mn> </msup> </mrow> <mn> 1172764769889007844720640000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 20737942737397933 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 18 </mn> </msup> </mrow> <mn> 11727647698890078447206400000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 206649295526133419 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 19 </mn> </msup> </mrow> <mn> 938211815911206275776512000000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 230932630430735533 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 20 </mn> </msup> </mrow> <mn> 4586813322232564014907392000000 </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'> 1 </cn> <cn type='integer'> -1 </cn> <cn type='rational'> -1 <sep /> 8 </cn> <cn type='rational'> 1 <sep /> 64 </cn> <cn type='rational'> -1 <sep /> 1536 </cn> <cn type='rational'> -11 <sep /> 36864 </cn> <cn type='rational'> 49 <sep /> 589824 </cn> <cn type='rational'> -55 <sep /> 9437184 </cn> <cn type='rational'> -83 <sep /> 35389440 </cn> <cn type='rational'> 12121 <sep /> 15099494400 </cn> <cn type='rational'> -114299 <sep /> 1630745395200 </cn> <cn type='rational'> -192151 <sep /> 7827577896960 </cn> <cn type='rational'> 83513957 <sep /> 8766887244595200 </cn> <cn type='rational'> -944750239 <sep /> 981891371394662400 </cn> <cn type='rational'> -27587714461 <sep /> 94261571653887590400 </cn> <cn type='rational'> 45487147753 <sep /> 361964435150928347136 </cn> <cn type='rational'> -11583279236477 <sep /> 814419979089588781056000 </cn> <cn type='rational'> -4401918060178787 <sep /> 1172764769889007844720640000 </cn> <cn type='rational'> 20737942737397933 <sep /> 11727647698890078447206400000 </cn> <cn type='rational'> -206649295526133419 <sep /> 938211815911206275776512000000 </cn> <cn type='rational'> -230932630430735533 <sep /> 4586813322232564014907392000000 </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'> 1 </cn> <ci> q </ci> </apply> <apply> <ci> SeriesData </ci> <ci> $CellContext`q </ci> <cn type='integer'> 0 </cn> <list> <cn type='integer'> 1 </cn> <cn type='integer'> -1 </cn> <cn type='rational'> -1 <sep /> 8 </cn> <cn type='rational'> 1 <sep /> 64 </cn> <cn type='rational'> -1 <sep /> 1536 </cn> <cn type='rational'> -11 <sep /> 36864 </cn> <cn type='rational'> 49 <sep /> 589824 </cn> <cn type='rational'> -55 <sep /> 9437184 </cn> <cn type='rational'> -83 <sep /> 35389440 </cn> <cn type='rational'> 12121 <sep /> 15099494400 </cn> <cn type='rational'> -114299 <sep /> 1630745395200 </cn> <cn type='rational'> -192151 <sep /> 7827577896960 </cn> <cn type='rational'> 83513957 <sep /> 8766887244595200 </cn> <cn type='rational'> -944750239 <sep /> 981891371394662400 </cn> <cn type='rational'> -27587714461 <sep /> 94261571653887590400 </cn> <cn type='rational'> 45487147753 <sep /> 361964435150928347136 </cn> <cn type='rational'> -11583279236477 <sep /> 814419979089588781056000 </cn> <cn type='rational'> -4401918060178787 <sep /> 1172764769889007844720640000 </cn> <cn type='rational'> 20737942737397933 <sep /> 11727647698890078447206400000 </cn> <cn type='rational'> -206649295526133419 <sep /> 938211815911206275776512000000 </cn> <cn type='rational'> -230932630430735533 <sep /> 4586813322232564014907392000000 </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["1", ",", "q_"]], "]"]], "]"]], "\[RuleDelayed]", InterpretationBox[RowBox[List["1", "-", "$CellContext`q", "-", RowBox[List[FractionBox["1", "8"], " ", SuperscriptBox["$CellContext`q", "2"]]], "+", RowBox[List[FractionBox["1", "64"], " ", SuperscriptBox["$CellContext`q", "3"]]], "-", RowBox[List[FractionBox["1", "1536"], " ", SuperscriptBox["$CellContext`q", "4"]]], "-", RowBox[List[FractionBox["11", "36864"], " ", SuperscriptBox["$CellContext`q", "5"]]], "+", RowBox[List[FractionBox["49", "589824"], " ", SuperscriptBox["$CellContext`q", "6"]]], "-", RowBox[List[FractionBox["55", "9437184"], " ", SuperscriptBox["$CellContext`q", "7"]]], "-", RowBox[List[FractionBox["83", "35389440"], " ", SuperscriptBox["$CellContext`q", "8"]]], "+", RowBox[List[FractionBox["12121", "15099494400"], " ", SuperscriptBox["$CellContext`q", "9"]]], "-", RowBox[List[FractionBox["114299", "1630745395200"], " ", SuperscriptBox["$CellContext`q", "10"]]], "-", RowBox[List[FractionBox["192151", "7827577896960"], " ", SuperscriptBox["$CellContext`q", "11"]]], "+", RowBox[List[FractionBox["83513957", "8766887244595200"], " ", SuperscriptBox["$CellContext`q", "12"]]], "-", RowBox[List[FractionBox["944750239", "981891371394662400"], " ", SuperscriptBox["$CellContext`q", "13"]]], "-", RowBox[List[FractionBox["27587714461", "94261571653887590400"], " ", SuperscriptBox["$CellContext`q", "14"]]], "+", RowBox[List[FractionBox["45487147753", "361964435150928347136"], " ", SuperscriptBox["$CellContext`q", "15"]]], "-", RowBox[List[FractionBox["11583279236477", "814419979089588781056000"], " ", SuperscriptBox["$CellContext`q", "16"]]], "-", RowBox[List[FractionBox["4401918060178787", "1172764769889007844720640000"], " ", SuperscriptBox["$CellContext`q", "17"]]], "+", RowBox[List[FractionBox["20737942737397933", "11727647698890078447206400000"], " ", SuperscriptBox["$CellContext`q", "18"]]], "-", RowBox[List[FractionBox["206649295526133419", "938211815911206275776512000000"], " ", SuperscriptBox["$CellContext`q", "19"]]], "-", RowBox[List[FractionBox["230932630430735533", "4586813322232564014907392000000"], " ", SuperscriptBox["$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[1, -1, Rational[-1, 8], Rational[1, 64], Rational[-1, 1536], Rational[-11, 36864], Rational[49, 589824], Rational[-55, 9437184], Rational[-83, 35389440], Rational[12121, 15099494400], Rational[-114299, 1630745395200], Rational[-192151, 7827577896960], Rational[83513957, 8766887244595200], Rational[-944750239, 981891371394662400], Rational[-27587714461, 94261571653887590400], Rational[45487147753, 361964435150928347136], Rational[-11583279236477, 814419979089588781056000], Rational[-4401918060178787, 1172764769889007844720640000], Rational[20737942737397933, 11727647698890078447206400000], Rational[-206649295526133419, 938211815911206275776512000000], Rational[-230932630430735533, 4586813322232564014907392000000]], 0, 21, 1], Rule[Editable, False]]]]]]










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





2001-10-29





© 1998- Wolfram Research, Inc.