Derivative of the even Mathieu function: Series representations (formula 11.03.06.0007)

MathieuCPrime

$Mathematica Notation$

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

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mi> Ce </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mrow> <mrow> <msub> <semantics> <mi> a </mi> <annotation-xml encoding='MathML-Content'> <ci> MathieuCharacteristicA </ci> </annotation-xml> </semantics> <mn> 3 </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> ∝ </mo> <semantics> <mrow> <mrow> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 5 </mn> <mn> 16 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mfrac> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 8 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> q </mi> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 64 </mn> </mfrac> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 15 </mn> <mn> 512 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 7 </mn> <mn> 640 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> q </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 4096 </mn> </mfrac> <mo> + </mo> <mrow> <mfrac> <mn> 3 </mn> <mn> 512 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mfrac> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 8192 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 5120 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> q </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 21 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mn> 32768 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 4863 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 13107200 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 16384 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 77 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 2949120 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 5160960 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> q </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 14061 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mn> 104857600 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 27 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 131072 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 12329 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 377487360 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 21 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 3276800 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 3670016 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 13 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 13 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 825753600 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> q </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 699 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mn> 838860800 </mn> </mfrac> </mrow> <mo> - </mo> <mfrac> <mrow> <mn> 13050583 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 181193932800 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 533 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 41943040 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 76679 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 75497472000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 17 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 235929600 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 6606028800 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 15 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 11890851840 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> q </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 31826419 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mn> 4348654387200 </mn> </mfrac> </mrow> <mo> - </mo> <mfrac> <mrow> <mn> 210369 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 33554432000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 326021051 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 60881161420800 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 9233 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 27179089920 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 7831 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 469762048000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 407 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 832359628800 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 13 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 13 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 2283043553280 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 17 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 17 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 49941577728000 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> q </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 300245939 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mn> 173946175488000 </mn> </mfrac> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 1193766593741 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 454579338608640000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 10194121 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 17394617548800 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 55617547 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 347892350976000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 30253 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 5919001804800 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 311971 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 1826434842624000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 221 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 13 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 106542032486400 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 15 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 213084064972800 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 19 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 19 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 17579435360256000 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> q </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 64306539779 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mn> 10909904126607360000 </mn> </mfrac> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 1087026917 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 1043677052928000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 767116375621 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 4363961650642944000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 468897223 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 24352464568320000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 21665887 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 8349416423424000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 84293 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 1704672519782400 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 2457689 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 13 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 2045607023738880000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 23 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 15 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 4602615803412480 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 17 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 17 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 281270965764096000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 21 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 361634098839552000 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> q </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 78221421983189 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mn> 785513097115729920000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 3555989290829 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 33249231623946240000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 1595308088447 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 19637827427893248000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 16802983705367 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 3366484701924556800000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 50000417 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 151526446202880000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 488862979 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 18410463213649920000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 1474993 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 13 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 4418511171275980800 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 74069 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 15 </mn> <mo> ⁢ </mo> <mi> z 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<times /> <cn type='rational'> -31826419 <sep /> 4348654387200 </cn> <apply> <sin /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> -210369 <sep /> 33554432000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 326021051 <sep /> 60881161420800 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -9233 <sep /> 27179089920 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -7831 <sep /> 469762048000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 9 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 407 <sep /> 832359628800 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 11 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -13 <sep /> 2283043553280 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 13 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 17 <sep /> 49941577728000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 17 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -300245939 <sep /> 173946175488000 </cn> <apply> <sin /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 1193766593741 <sep /> 454579338608640000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 10194121 <sep /> 17394617548800 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -55617547 <sep /> 347892350976000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 30253 <sep /> 5919001804800 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 9 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 311971 <sep /> 1826434842624000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 11 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -221 <sep /> 106542032486400 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 13 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 213084064972800 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 15 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -19 <sep /> 17579435360256000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 19 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -64306539779 <sep /> 10909904126607360000 </cn> <apply> <sin /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 1087026917 <sep /> 1043677052928000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -767116375621 <sep /> 4363961650642944000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -468897223 <sep /> 24352464568320000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 21665887 <sep /> 8349416423424000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 9 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -84293 <sep /> 1704672519782400 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 11 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -2457689 <sep /> 2045607023738880000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 13 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 23 <sep /> 4602615803412480 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 15 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 17 <sep /> 281270965764096000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 17 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 361634098839552000 </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'> 78221421983189 <sep /> 785513097115729920000 </cn> <apply> <sin /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 3555989290829 <sep /> 33249231623946240000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1595308088447 <sep /> 19637827427893248000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 16802983705367 <sep /> 3366484701924556800000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 50000417 <sep /> 151526446202880000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 9 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -488862979 <sep /> 18410463213649920000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 11 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1474993 <sep /> 4418511171275980800 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 13 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 74069 <sep /> 12000894539268096000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 15 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -17 <sep /> 13807847410237440000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 17 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -19 <sep /> 48603622884035788800 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 19 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -23 <sep /> 3949044359327907840000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 23 </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'> 3 </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'> -3 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -1 <sep /> 8 </cn> <apply> <sin /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 5 <sep /> 16 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -1 <sep /> 64 </cn> <apply> <sin /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 15 <sep /> 512 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -7 <sep /> 640 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 4096 </cn> <apply> <sin /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 3 <sep /> 512 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -11 <sep /> 8192 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 5120 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 9 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 21 <sep /> 32768 </cn> <apply> <sin /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 4863 <sep /> 13107200 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -5 <sep /> 16384 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 77 <sep /> 2949120 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -11 <sep /> 5160960 </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'> 14061 <sep /> 104857600 </cn> <apply> <sin /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> -27 <sep /> 131072 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -12329 <sep /> 377487360 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 21 <sep /> 3276800 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 3670016 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 9 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 13 <sep /> 825753600 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 13 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -699 <sep /> 838860800 </cn> <apply> <sin /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> -13050583 <sep /> 181193932800 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 533 <sep /> 41943040 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 76679 <sep /> 75497472000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -17 <sep /> 235929600 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 9 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 11 <sep /> 6606028800 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 11 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 11890851840 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 15 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -31826419 <sep /> 4348654387200 </cn> <apply> <sin /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> -210369 <sep /> 33554432000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 326021051 <sep /> 60881161420800 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -9233 <sep /> 27179089920 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -7831 <sep /> 469762048000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 9 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 407 <sep /> 832359628800 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 11 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -13 <sep /> 2283043553280 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 13 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 17 <sep /> 49941577728000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 17 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -300245939 <sep /> 173946175488000 </cn> <apply> <sin /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 1193766593741 <sep /> 454579338608640000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 10194121 <sep /> 17394617548800 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -55617547 <sep /> 347892350976000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 30253 <sep /> 5919001804800 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 9 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 311971 <sep /> 1826434842624000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 11 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -221 <sep /> 106542032486400 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 13 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 213084064972800 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 15 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -19 <sep /> 17579435360256000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 19 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -64306539779 <sep /> 10909904126607360000 </cn> <apply> <sin /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 1087026917 <sep /> 1043677052928000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -767116375621 <sep /> 4363961650642944000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -468897223 <sep /> 24352464568320000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 21665887 <sep /> 8349416423424000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 9 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -84293 <sep /> 1704672519782400 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 11 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -2457689 <sep /> 2045607023738880000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 13 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 23 <sep /> 4602615803412480 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 15 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 17 <sep /> 281270965764096000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 17 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 361634098839552000 </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'> 78221421983189 <sep /> 785513097115729920000 </cn> <apply> <sin /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 3555989290829 <sep /> 33249231623946240000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1595308088447 <sep /> 19637827427893248000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 16802983705367 <sep /> 3366484701924556800000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 50000417 <sep /> 151526446202880000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 9 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -488862979 <sep /> 18410463213649920000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 11 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1474993 <sep /> 4418511171275980800 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 13 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 74069 <sep /> 12000894539268096000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 15 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -17 <sep /> 13807847410237440000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 17 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -19 <sep /> 48603622884035788800 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 19 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -23 <sep /> 3949044359327907840000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 23 </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> </apply> </annotation-xml> </semantics> </math>

Rule Form

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

2001-10-29