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MathieuS






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/11.02.06.0004.01









  


  










Input Form





MathieuS[MathieuCharacteristicB[1, q], q, z] \[Proportional] Sin[z] - (1/8) Sin[3 z] q + (-(Sin[z]/128) + (1/64) Sin[3 z] + (1/192) Sin[5 z]) q^2 + (Sin[z]/512 + Sin[3 z]/3072 - Sin[5 z]/1152 - Sin[7 z]/9216) q^3 + (-((37 Sin[z])/294912) - (49 Sin[3 z])/73728 + Sin[7 z]/49152 + Sin[9 z]/737280) q^4 + (-((121 Sin[z])/1769472) + (317 Sin[3 z])/2359296 + (41 Sin[5 z])/1179648 - Sin[7 z]/5898240 - Sin[9 z]/3686400 - Sin[11 z]/88473600) q^5 + ((8105 Sin[z])/339738624 + (103 Sin[3 z])/56623104 - (731 Sin[5 z])/94371840 - (379 Sin[7 z])/471859200 + Sin[9 z]/283115520 + Sin[11 z]/424673280 + Sin[13 z]/14863564800) q^6 + (-((481 Sin[z])/226492416) - (102547 Sin[3 z])/13589544960 + (659 Sin[5 z])/11324620800 + (12677 Sin[7 z])/67947724800 + (181 Sin[9 z])/16986931200 - Sin[11 z]/26424115200 - Sin[13 z]/69363302400 - Sin[15 z]/3329438515200) q^7 + (-((1237783 Sin[z])/1449551462400) + (940781 Sin[3 z])/543581798400 + (322897 Sin[5 z])/815372697600 - (9413 Sin[7 z])/3261490790400 - (2143 Sin[9 z])/845571686400 - (1229 Sin[11 z])/13317754060800 + Sin[13 z]/3805072588800 + Sin[15 z]/15220290355200 + Sin[17 z]/958878292377600) q^8 + ((11221967 Sin[z])/32614907904000 + (506831 Sin[3 z])/104367705292800 - (310133 Sin[5 z])/3131031158784 - (5039101 Sin[7 z])/547930452787200 + (16013 Sin[9 z])/319626097459200 + (3167 Sin[11 z])/142056043315200 + (481 Sin[13 z])/852336259891200 - Sin[15 z]/767102633902080 - Sin[17 z]/4314952315699200 - Sin[19 z]/345196185255936000) q^9 + (-((4539285691 Sin[z])/125241246351360000) - (1282939901 Sin[3 z])/ 12524124635136000 + (10304813 Sin[5 z])/5844591496396800 + (48740801 Sin[7 z])/20456070237388800 + (7516703 Sin[9 z])/ 61368210712166400 - (30773 Sin[11 z])/61368210712166400 - (25379 Sin[13 z])/184104632136499200 - (2839 Sin[15 z])/ 1104627792818995200 + Sin[17 z]/204560702373888000 + Sin[19 z]/1534205267804160000 + Sin[21 z]/151886321512611840000) q^10 + SeriesData[$CellContext`q, 0, {}, 0, 11, 1]










Standard Form





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MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> Se </mi> <mo> &#8289; </mo> <mo> ( </mo> <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> , </mo> <mi> q </mi> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 4539285691 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mn> 125241246351360000 </mn> </mfrac> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 10304813 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 5844591496396800 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 48740801 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 20456070237388800 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 7516703 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 61368210712166400 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 17 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 204560702373888000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 19 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 1534205267804160000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 21 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 151886321512611840000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 1282939901 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 12524124635136000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 30773 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 11 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 61368210712166400 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 25379 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 13 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 184104632136499200 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 2839 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 15 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 1104627792818995200 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 10 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 11221967 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mn> 32614907904000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 506831 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 104367705292800 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 16013 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 319626097459200 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 3167 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 11 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 142056043315200 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 481 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 13 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 852336259891200 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 310133 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 3131031158784 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 5039101 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 547930452787200 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 15 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 767102633902080 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 17 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 4314952315699200 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 19 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 345196185255936000 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 1237783 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mn> 1449551462400 </mn> </mfrac> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 940781 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 543581798400 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 322897 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 815372697600 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 13 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 3805072588800 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 15 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 15220290355200 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 17 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 958878292377600 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 2143 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> 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Rule Form





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





2001-10-29





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