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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/11.03.06.0007.01









  


  










Input Form





MathieuCPrime[MathieuCharacteristicA[3, q], q, z] \[Proportional] -(3 Sin[3 z]) + (-(Sin[z]/8) + (5/16) Sin[5 z]) q + (-(Sin[z]/64) + (15/512) Sin[3 z] - (7/640) Sin[7 z]) q^2 + (Sin[z]/4096 + (3/512) Sin[3 z] - (11 Sin[5 z])/8192 + Sin[9 z]/5120) q^3 + ((21 Sin[z])/32768 + (4863 Sin[3 z])/13107200 - (5 Sin[5 z])/16384 + (77 Sin[7 z])/2949120 - (11 Sin[11 z])/5160960) q^4 + ((14061 Sin[z])/104857600 - (27 Sin[3 z])/131072 - (12329 Sin[5 z])/377487360 + (21 Sin[7 z])/3276800 - Sin[9 z]/3670016 + (13 Sin[13 z])/825753600) q^5 + (-((699 Sin[z])/838860800) - (13050583 Sin[3 z])/181193932800 + (533 Sin[5 z])/41943040 + (76679 Sin[7 z])/75497472000 - (17 Sin[9 z])/235929600 + (11 Sin[11 z])/6606028800 - Sin[15 z]/11890851840) q^6 + (-((31826419 Sin[z])/4348654387200) - (210369 Sin[3 z])/33554432000 + (326021051 Sin[5 z])/60881161420800 - (9233 Sin[7 z])/27179089920 - (7831 Sin[9 z])/469762048000 + (407 Sin[11 z])/832359628800 - (13 Sin[13 z])/2283043553280 + (17 Sin[17 z])/49941577728000) q^7 + (-((300245939 Sin[z])/173946175488000) + (1193766593741 Sin[3 z])/ 454579338608640000 + (10194121 Sin[5 z])/17394617548800 - (55617547 Sin[7 z])/347892350976000 + (30253 Sin[9 z])/5919001804800 + (311971 Sin[11 z])/1826434842624000 - (221 Sin[13 z])/106542032486400 + Sin[15 z]/213084064972800 - (19 Sin[19 z])/17579435360256000) q^8 + (-((64306539779 Sin[z])/10909904126607360000) + (1087026917 Sin[3 z])/1043677052928000 - (767116375621 Sin[5 z])/ 4363961650642944000 - (468897223 Sin[7 z])/24352464568320000 + (21665887 Sin[9 z])/8349416423424000 - (84293 Sin[11 z])/ 1704672519782400 - (2457689 Sin[13 z])/2045607023738880000 + (23 Sin[15 z])/4602615803412480 + (17 Sin[17 z])/281270965764096000 + Sin[21 z]/361634098839552000) q^9 + ((78221421983189 Sin[z])/785513097115729920000 + (3555989290829 Sin[3 z])/33249231623946240000 - (1595308088447 Sin[5 z])/19637827427893248000 + (16802983705367 Sin[7 z])/3366484701924556800000 + (50000417 Sin[9 z])/151526446202880000 - (488862979 Sin[11 z])/ 18410463213649920000 + (1474993 Sin[13 z])/4418511171275980800 + (74069 Sin[15 z])/12000894539268096000 - (17 Sin[17 z])/ 13807847410237440000 - (19 Sin[19 z])/48603622884035788800 - (23 Sin[23 z])/3949044359327907840000) q^10 + SeriesData[$CellContext`q, 0, {}, 0, 11, 1]










Standard Form





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MathML Form







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Rule Form





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





2001-10-29





© 1998- Wolfram Research, Inc.