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MathieuCPrime






Mathematica Notation

Traditional Notation









Mathieu and Spheroidal Functions > MathieuCPrime[a,q,z] > Series representations > Generalized power series > Expansions at q==0





http://functions.wolfram.com/11.03.06.0010.01









  


  










Input Form





MathieuCPrime[MathieuCharacteristicA[6, q], q, z] \[Proportional] -(6 Sin[6 z]) + ((-(1/5)) Sin[4 z] + (2/7) Sin[8 z]) q + ((-(1/320)) Sin[2 z] + (111 Sin[6 z])/9800 - (5/896) Sin[10 z]) q^2 + ((163 Sin[4 z])/784000 - (257 Sin[8 z])/1097600 + Sin[12 z]/16128) q^3 + (-((353 Sin[2 z])/451584000) - (286737 Sin[6 z])/98344960000 + (239 Sin[10 z])/94832640 - Sin[14 z]/2211840) q^4 + (-((2489531 Sin[4 z])/8851046400000) - (170407 Sin[8 z])/18587197440000 - (41 Sin[12 z])/2528870400 + Sin[16 z]/425779200) q^5 + (-((1605431 Sin[2 z])/566466969600000) + (4710167167 Sin[6 z])/ 117099343872000000 + (553237 Sin[10 z])/951664508928000 + (31 Sin[14 z])/476872704000 - Sin[18 z]/108999475200) q^6 + ((218043962237 Sin[4 z])/112415370117120000000 - (193876801753 Sin[8 z])/157381518163968000000 - (232901 Sin[12 z])/34894365327360000 - (89 Sin[16 z])/600859607040000 + Sin[20 z]/35708228075520) q^7 + ((245823431717 Sin[2 z])/7194583687495680000000 - (1063920412095787 Sin[6 z])/9400922684994355200000000 + (200739663361 Sin[10 z])/11079658878743347200000 + (1862617 Sin[14 z])/43069616632627200000 + Sin[18 z]/27773066280960000 - Sin[22 z]/14542987434393600) q^8 + (-((969576234653531 Sin[4 z])/282027680549830656000000000) + (5672082905031097 Sin[8 z])/2171613140233696051200000000 - (214745589353 Sin[12 z])/1329559065449201664000000 - (1851407 Sin[16 z])/9798337783922688000000 + Sin[20 z]/861392332652544000 + Sin[24 z]/7198778780024832000) q^9 + (-((751507595970539 Sin[2 z])/162447943996702457856000000000) + (3216652896139146931 Sin[6 z])/22295228239732612792320000000000 - (33253071721431293 Sin[10 z])/1000679335019687140392960000000 + (580342764629 Sin[14 z])/592603469171644170240000000 + (167383 Sin[18 z])/278708274742689792000000 - (41 Sin[22 z])/7696148950281093120000 - Sin[26 z]/4252817002353131520000) q^10 + SeriesData[$CellContext`q, 0, {}, 0, 11, 1]










Standard Form





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MathML Form







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$CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 23 <sep /> 69108276288238387200 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 23 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1135692325 <sep /> 3325548247949154189312 </cn> <apply> <sin /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 592465 <sep /> 1099718335962021888 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -18970709026319 <sep /> 1662774123974577094656000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -13721 <sep /> 117826964567359488 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 21353891011 <sep /> 71129781970023575715840 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 9 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 6919 <sep /> 75745905793302528 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 11 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 112350719 <sep /> 48992451867108075110400 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 13 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1123 <sep /> 1841046321364992000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 15 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 187 <sep /> 29784038265638092800 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 17 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 42123139832831016960 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 21 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 1658598630917721292800 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 25 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> </list> <cn type='integer'> 0 </cn> <cn type='integer'> 11 </cn> <cn type='integer'> 1 </cn> </apply> </annotation-xml> </semantics> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportional </ci> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 1 </cn> </list> <ci> Ce </ci> </apply> <apply> <ci> MathieuCharacteristicA </ci> <cn type='integer'> 6 </cn> <ci> q </ci> </apply> <ci> q </ci> <ci> z </ci> </apply> <apply> <ci> SeriesData </ci> <ci> $CellContext`q </ci> <cn type='integer'> 0 </cn> <list> <apply> <times /> <cn type='integer'> -5 </cn> <apply> <sin /> 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/> <cn type='rational'> -1 <sep /> 9216 </cn> <apply> <sin /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 7 <sep /> 24576 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -13 <sep /> 36864 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 11 <sep /> 129024 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 11 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 589824 </cn> <apply> <sin /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 49152 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn 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<apply> <times /> <cn type='integer'> 7 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 294521 <sep /> 11932707638476800 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 9 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -253 <sep /> 12785043898368 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 11 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 3609307 <sep /> 10632042505882828800 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 13 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -17 <sep /> 31642983648460800 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 17 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 6529504562380800 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 21 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -187567 <sep /> 29456741141839872 </cn> <apply> <sin /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 889319687 <sep /> 15396056703468306432 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 7955 <sep /> 424274049368064 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -10349972261 <sep /> 742309876774364774400 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -157 <sep /> 17046725197824 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 9 </cn> <ci> $CellContext`z </ci> </apply> </apply> 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<plus /> <apply> <times /> <cn type='rational'> 1135692325 <sep /> 3325548247949154189312 </cn> <apply> <sin /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 592465 <sep /> 1099718335962021888 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -18970709026319 <sep /> 1662774123974577094656000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -13721 <sep /> 117826964567359488 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 21353891011 <sep /> 71129781970023575715840 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 9 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 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Date Added to functions.wolfram.com (modification date)





2001-10-29





© 1998-2014 Wolfram Research, Inc.