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MathieuCharacteristicA






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/11.05.06.0011.01









  


  










Input Form





MathieuCharacteristicA[9, q] \[Proportional] SeriesData[$CellContext`q, 0, {81, 0, Rational[1, 160], 0, Rational[103, 315392000], 0, Rational[1993, 36333158400000], 0, Rational[425125339, 28676616703967232000000], Rational[1, 106542032486400], Rational[1130345443, 203922607672655872000000000], Rational[-11, 2727476031651840000], Rational[62629265104555151, 22563907986167495394538291200000000000], Rational[31447, 68997143004432039936000000], Rational[80555146157400451, 41259717460420563007155732480000000000000], Rational[-7339639, 171686970880788333613547520000000], Rational[405059575281583710161972141, 167926821562095099968656489164199428096000000000000000], Rational[-15120710271341, 2201990611321866125684585325920256000000000], Rational[-11523405880011634059270211650029, 940175254416133078096516459013386622069637120000000000000000], Rational[-145650578734543, 31317199805466540454180769079754752000000000000], Rational[15089819507835055103567092482603681329, 1936670767272810192103326639987511156347733782036480000000000000000000]}, 0, 21, 1]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["MathieuCharacteristicA", "[", RowBox[List["9", ",", "q"]], "]"]], "\[Proportional]", InterpretationBox[RowBox[List["81", "+", FractionBox[SuperscriptBox["q", "2"], "160"], "+", FractionBox[RowBox[List["103", " ", SuperscriptBox["q", "4"]]], "315392000"], "+", FractionBox[RowBox[List["1993", " ", SuperscriptBox["q", "6"]]], "36333158400000"], "+", FractionBox[RowBox[List["425125339", " ", SuperscriptBox["q", "8"]]], "28676616703967232000000"], "+", FractionBox[SuperscriptBox["q", "9"], "106542032486400"], "+", FractionBox[RowBox[List["1130345443", " ", SuperscriptBox["q", "10"]]], "203922607672655872000000000"], "-", FractionBox[RowBox[List["11", " ", SuperscriptBox["q", "11"]]], "2727476031651840000"], "+", FractionBox[RowBox[List["62629265104555151", " ", SuperscriptBox["q", "12"]]], "22563907986167495394538291200000000000"], "+", FractionBox[RowBox[List["31447", " ", SuperscriptBox["q", "13"]]], "68997143004432039936000000"], "+", FractionBox[RowBox[List["80555146157400451", " ", SuperscriptBox["q", "14"]]], "41259717460420563007155732480000000000000"], "-", FractionBox[RowBox[List["7339639", " ", SuperscriptBox["q", "15"]]], "171686970880788333613547520000000"], "+", RowBox[List[RowBox[List["(", RowBox[List["405059575281583710161972141", " ", SuperscriptBox["q", "16"]]], ")"]], "/", "167926821562095099968656489164199428096000000000000000"]], "-", FractionBox[RowBox[List["15120710271341", " ", SuperscriptBox["q", "17"]]], "2201990611321866125684585325920256000000000"], "-", RowBox[List[RowBox[List["(", RowBox[List["11523405880011634059270211650029", " ", SuperscriptBox["q", "18"]]], ")"]], "/", "940175254416133078096516459013386622069637120000000000000000"]], "-", FractionBox[RowBox[List["145650578734543", " ", SuperscriptBox["q", "19"]]], "31317199805466540454180769079754752000000000000"], "+", RowBox[List[RowBox[List["(", RowBox[List["15089819507835055103567092482603681329", " ", SuperscriptBox["q", "20"]]], ")"]], "/", "1936670767272810192103326639987511156347733782036480000000000000000000"]], "+", InterpretationBox[SuperscriptBox[RowBox[List["O", "[", "q", "]"]], "21"], SeriesData[$CellContext`q, 0, List[], 0, 21, 1]]]], SeriesData[$CellContext`q, 0, List[81, 0, Rational[1, 160], 0, Rational[103, 315392000], 0, Rational[1993, 36333158400000], 0, Rational[425125339, 28676616703967232000000], Rational[1, 106542032486400], Rational[1130345443, 203922607672655872000000000], Rational[-11, 2727476031651840000], Rational[62629265104555151, 22563907986167495394538291200000000000], Rational[31447, 68997143004432039936000000], Rational[80555146157400451, 41259717460420563007155732480000000000000], Rational[-7339639, 171686970880788333613547520000000], Rational[405059575281583710161972141, 167926821562095099968656489164199428096000000000000000], Rational[-15120710271341, 2201990611321866125684585325920256000000000], Rational[-11523405880011634059270211650029, 940175254416133078096516459013386622069637120000000000000000], Rational[-145650578734543, 31317199805466540454180769079754752000000000000], Rational[15089819507835055103567092482603681329, 1936670767272810192103326639987511156347733782036480000000000000000000]], 0, 21, 1]]]]]]










MathML Form







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</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'> 81 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 160 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 103 <sep /> 315392000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1993 <sep /> 36333158400000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 425125339 <sep /> 28676616703967232000000 </cn> <cn type='rational'> 1 <sep /> 106542032486400 </cn> <cn type='rational'> 1130345443 <sep /> 203922607672655872000000000 </cn> <cn type='rational'> -11 <sep /> 2727476031651840000 </cn> <cn type='rational'> 62629265104555151 <sep /> 22563907986167495394538291200000000000 </cn> <cn type='rational'> 31447 <sep /> 68997143004432039936000000 </cn> <cn type='rational'> 80555146157400451 <sep /> 41259717460420563007155732480000000000000 </cn> <cn type='rational'> -7339639 <sep /> 171686970880788333613547520000000 </cn> <cn type='rational'> 405059575281583710161972141 <sep /> 167926821562095099968656489164199428096000000000000000 </cn> <cn type='rational'> -15120710271341 <sep /> 2201990611321866125684585325920256000000000 </cn> <cn type='rational'> -11523405880011634059270211650029 <sep /> 940175254416133078096516459013386622069637120000000000000000 </cn> <cn type='rational'> -145650578734543 <sep /> 31317199805466540454180769079754752000000000000 </cn> <cn type='rational'> 15089819507835055103567092482603681329 <sep /> 1936670767272810192103326639987511156347733782036480000000000000000000 </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'> 9 </cn> <ci> q </ci> </apply> <apply> <ci> SeriesData </ci> <ci> $CellContext`q </ci> <cn type='integer'> 0 </cn> <list> <cn type='integer'> 81 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 160 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 103 <sep /> 315392000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1993 <sep /> 36333158400000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 425125339 <sep /> 28676616703967232000000 </cn> <cn type='rational'> 1 <sep /> 106542032486400 </cn> <cn type='rational'> 1130345443 <sep /> 203922607672655872000000000 </cn> <cn type='rational'> -11 <sep /> 2727476031651840000 </cn> <cn type='rational'> 62629265104555151 <sep /> 22563907986167495394538291200000000000 </cn> <cn type='rational'> 31447 <sep /> 68997143004432039936000000 </cn> <cn type='rational'> 80555146157400451 <sep /> 41259717460420563007155732480000000000000 </cn> <cn type='rational'> -7339639 <sep /> 171686970880788333613547520000000 </cn> <cn type='rational'> 405059575281583710161972141 <sep /> 167926821562095099968656489164199428096000000000000000 </cn> <cn type='rational'> -15120710271341 <sep /> 2201990611321866125684585325920256000000000 </cn> <cn type='rational'> -11523405880011634059270211650029 <sep /> 940175254416133078096516459013386622069637120000000000000000 </cn> <cn type='rational'> -145650578734543 <sep /> 31317199805466540454180769079754752000000000000 </cn> <cn type='rational'> 15089819507835055103567092482603681329 <sep /> 1936670767272810192103326639987511156347733782036480000000000000000000 </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["MathieuCharacteristicA", "[", RowBox[List["9", ",", "q_"]], "]"]], "]"]], "\[RuleDelayed]", InterpretationBox[RowBox[List["81", "+", RowBox[List[FractionBox["1", "160"], " ", SuperscriptBox["$CellContext`q", "2"]]], "+", RowBox[List[FractionBox["103", "315392000"], " ", SuperscriptBox["$CellContext`q", "4"]]], "+", RowBox[List[FractionBox["1993", "36333158400000"], " ", SuperscriptBox["$CellContext`q", "6"]]], "+", RowBox[List[FractionBox["425125339", "28676616703967232000000"], " ", SuperscriptBox["$CellContext`q", "8"]]], "+", RowBox[List[FractionBox["1", "106542032486400"], " ", SuperscriptBox["$CellContext`q", "9"]]], "+", RowBox[List[FractionBox["1130345443", "203922607672655872000000000"], " ", SuperscriptBox["$CellContext`q", "10"]]], "-", RowBox[List[FractionBox["11", "2727476031651840000"], " ", SuperscriptBox["$CellContext`q", "11"]]], "+", RowBox[List[FractionBox["62629265104555151", "22563907986167495394538291200000000000"], " ", SuperscriptBox["$CellContext`q", "12"]]], "+", RowBox[List[FractionBox["31447", "68997143004432039936000000"], " ", SuperscriptBox["$CellContext`q", "13"]]], "+", RowBox[List[FractionBox["80555146157400451", "41259717460420563007155732480000000000000"], " ", SuperscriptBox["$CellContext`q", "14"]]], "-", RowBox[List[FractionBox["7339639", "171686970880788333613547520000000"], " ", SuperscriptBox["$CellContext`q", "15"]]], "+", RowBox[List[FractionBox["405059575281583710161972141", "167926821562095099968656489164199428096000000000000000"], " ", SuperscriptBox["$CellContext`q", "16"]]], "-", RowBox[List[FractionBox["15120710271341", "2201990611321866125684585325920256000000000"], " ", SuperscriptBox["$CellContext`q", "17"]]], "-", RowBox[List[FractionBox["11523405880011634059270211650029", "940175254416133078096516459013386622069637120000000000000000"], " ", SuperscriptBox["$CellContext`q", "18"]]], "-", RowBox[List[FractionBox["145650578734543", "31317199805466540454180769079754752000000000000"], " ", SuperscriptBox["$CellContext`q", "19"]]], "+", RowBox[List[FractionBox["15089819507835055103567092482603681329", "1936670767272810192103326639987511156347733782036480000000000000000000"], " ", SuperscriptBox["$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[81, 0, Rational[1, 160], 0, Rational[103, 315392000], 0, Rational[1993, 36333158400000], 0, Rational[425125339, 28676616703967232000000], Rational[1, 106542032486400], Rational[1130345443, 203922607672655872000000000], Rational[-11, 2727476031651840000], Rational[62629265104555151, 22563907986167495394538291200000000000], Rational[31447, 68997143004432039936000000], Rational[80555146157400451, 41259717460420563007155732480000000000000], Rational[-7339639, 171686970880788333613547520000000], Rational[405059575281583710161972141, 167926821562095099968656489164199428096000000000000000], Rational[-15120710271341, 2201990611321866125684585325920256000000000], Rational[-11523405880011634059270211650029, 940175254416133078096516459013386622069637120000000000000000], Rational[-145650578734543, 31317199805466540454180769079754752000000000000], Rational[15089819507835055103567092482603681329, 1936670767272810192103326639987511156347733782036480000000000000000000]], 0, 21, 1], Rule[Editable, False]]]]]]










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





2001-10-29





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