Legend:
f
(x) = sin°0.5(x) \\ =
"half-iterate" of sin(x)
k : index
of coefficient
ck : coefficient of the formal
powerseries for sin°0.5(x) at xk
Computed by "SI05 = trisqrt(SI)" where SI is the bell-matrix for sin(x)
|
k |
log10( |ck| ) |
ck |
|
1 |
0.E-202 |
1.0000000000000000000000000000000000000000000000000 |
|
3 |
-1.07918124605 |
-0.083333333333333333333333333333333333333333333333333 |
|
5 |
-2.20411998266 |
-0.0062500000000000000000000000000000000000000000000000 |
|
7 |
-2.88124465384 |
-0.0013144841269841269841269841269841269841269841269841 |
|
9 |
-3.49367016064 |
-0.00032087053571428571428571428571428571428571428571429 |
|
11 |
-4.13916506218 |
-0.000072583003898108064774731441398108064774731441398108 |
|
13 |
-5.03106823676 |
-0.0000093096159041254527365638476749587860698971810082921 |
|
15 |
-5.44943122357 |
0.0000035527837718063309167806522303876801231298585795940 |
|
17 |
-5.44162900239 |
0.0000036171873021448378799435541576842541672918268000745 |
|
19 |
-5.77528253450 |
0.0000016777122110338958019154927860742870307449875469416 |
|
21 |
-6.42615913867 |
0.00000037483562593959494861486753457222064851384718816205 |
|
23 |
-7.00412877933 |
-0.000000099053818164382719492695381188844251823336314000265 |
|
25 |
-6.92261276513 |
-0.00000011950531882560049596433442673788675358865970085316 |
|
27 |
-7.61665790243 |
-0.000000024173642637156755904452095150360703777443292399847 |
|
29 |
-7.56725226875 |
0.000000027086178192874224577638725258999298308962229230845 |
|
31 |
-7.74598584949 |
0.000000017947921051353670827546570628514621543886801027566 |
|
33 |
-8.12489198502 |
-0.0000000075008074147802738169737628174124038311009386204632 |
|
35 |
-7.86266536924 |
-0.000000013719384592627801708047919594410263499394988187869 |
|
37 |
-9.22596608170 |
-0.00000000059433857450346597260631595806697385230305351242860 |
|
39 |
-7.99297156484 |
0.000000010163152332981341600349709888182971120246007740333 |
|
41 |
-8.32723632446 |
0.0000000047072111041813835504174714784445383874402981343211 |
|
43 |
-8.11270224983 |
-0.0000000077143217793171717146777601300530526774113728843882 |
|
45 |
-8.08969055051 |
-0.0000000081340989175603496454575766054358962043868815211225 |
|
47 |
-8.24489391466 |
0.0000000056899190182162768794817811772649674804324149649483 |
|
49 |
-7.89268186864 |
0.000000012803188256862008679755370445468908521459964356386 |
|
51 |
-8.55375554000 |
-0.0000000027941161785652732567716280631941310380266552796575 |
|
53 |
-7.68035489748 |
-0.000000020875894937933306286353945138219684410932416769515 |
|
55 |
-8.41449610797 |
-0.0000000038503826527558923987173014512125980634044712873027 |
|
57 |
-7.43933305358 |
0.000000036363606241550613669120367451801354528172875736854 |
|
59 |
-7.64946409919 |
0.000000022414853297640175158033850963467762343422191671977 |
|
61 |
-7.16886893434 |
-0.000000067784604379017274955034043156532492407248857184179 |
|
63 |
-7.10444377108 |
-0.000000078624198078634519980499036243767786656336437925768 |
|
65 |
-6.87582705859 |
0.00000013309843268110889793121382997277676421806018144437 |
|
67 |
-6.58645434078 |
0.00000025914668589371816279706861454963965328133349231525 |
|
69 |
-6.57772325333 |
-0.00000026440931233220142713139699294566493789195756224843 |
|
71 |
-6.05803074706 |
-0.00000087492183057169917026790006485459059528805515216173 |
|
73 |
-6.32282669772 |
0.00000047552494309980024433107617263436624188207667123836 |
|
75 |
-5.50670843949 |
0.0000031138060671248010080376271344371765991784507158656 |
|
77 |
-6.38353510298 |
-0.00000041348989160114642239221045870049991049752470650792 |
|
79 |
-4.92790511468 |
-0.000011805785420794244453613117703087293626743732457983 |
|
81 |
-5.49890661326 |
-0.0000031702490912834019640889521256114826478563534882066 |
|
83 |
-4.32039981537 |
0.000047818966395839854213573597383870443894655992612195 |
|
85 |
-4.47729578408 |
0.000033319940401492228947540775845694955440438445090095 |
|
87 |
-3.68478776733 |
-0.00020663897202709049289264497446859570056604189476791 |
|
89 |
-3.61074557173 |
-0.00024504984281018979987259479914725880565671817663025 |
|
91 |
-3.02296654555 |
0.00094849152441023724609617409277772078556653161790360 |
|
93 |
-2.77283154355 |
0.0016872073414141052183750561236881835761456355519476 |
|
95 |
-2.33816883615 |
-0.0045901952989870258411237376432912971135897199315799 |
|
97 |
-1.93280641663 |
-0.011673298292511154777553654070147021850523246050237 |
|
99 |
-1.63555788474 |
0.023144196890846764059946014254463947981649400245413 |
|
101 |
-1.07896090894 |
0.083375622805505018657156574838611607611614184649020 |
|
103 |
-0.923931218472 |
-0.11914306863035655706684393546778356787987417330108 |
|
105 |
-0.206009403672 |
-0.62228681079970868995954762498540720373588649851541 |
|
107 |
-0.220722653007 |
0.60155777869442208518678855507052660384494405041586 |
|
109 |
0.688563660693 |
4.8816165277004310487716373392545799442633519982650 |
|
111 |
0.428437526524 |
-2.6818687917089740330894184863303882737561150154574 |
|
113 |
1.60588716309 |
-40.354053281824939349333559524290224372220270268027 |
|
115 |
0.781535025540 |
6.0469311744600464939753423783132717407226258947765 |
|
117 |
2.54631792619 |
351.81789530957303379731739176529951103498619067978 |
|
119 |
1.94525208960 |
88.156043310589218528552787069535314950345482136436 |
|
121 |
3.50974219824 |
-3234.0162534542727043863134617252333603658926508329 |
|
123 |
3.33379524327 |
-2156.7273376408991572773193950744229598856661280743 |
|
125 |
4.49573062457 |
31313.428755455424235141155347772987868946588944601 |
|
127 |
4.54232296727 |
34859.645577275969113262459992091832989269936490385 |
|
129 |
5.50361529992 |
-318871.20276914850701975362944738132561695121133077 |
|
131 |
5.70909355146 |
-511792.06889891589274828577920745589622823878158920 |
|
133 |
6.53251833400 |
3408147.1219074151592413757655400359096662863047413 |
|
135 |
6.86713819657 |
7364414.0276039720736247731134364377294925847534757 |
|
137 |
7.58134252955 |
-38136648.986819253429321737669136698146791186953879 |
|
139 |
8.02933428591 |
-106987807.08001154308836825204569382516940517090359 |
|
141 |
8.64872232804 |
445371403.21539402420546951030580752475770465125767 |
|
143 |
9.20183980608 |
1591621533.0423000766617014136275492572791768083724 |
|
145 |
9.73291966115 |
-5406542996.5991275646885425000669999345823899464983 |
|
147 |
10.3879278711 |
-24430247740.800493203990540128361127348720094543135 |
|
149 |
10.8316262536 |
67861937297.068010446588773124399188553481203749423 |
|
151 |
11.5894313177 |
388536047335.23901159130598863653463865073786529461 |
|
153 |
11.9415825822 |
-874143197405.81455121303399425807246793843918895355 |
|
155 |
12.8073875186 |
-6417819797342.5714341294728939998766363682007943125 |
|
157 |
13.0577884753 |
11423218274247.661369047399434051588921700830052731 |
|
159 |
14.0423615459 |
110245671193349.59115936637776312175910684660638634 |
|
161 |
14.1716579489 |
-148476577760022.98809853629525144318146410908310327 |
|
163 |
15.2946223235 |
-1970708199083628.1286295000633407098193773325739892 |
|
165 |
15.2658094182 |
1844205947062533.4105617350397283825270690045356501 |
|
167 |
16.5642448697 |
36664424259463075.564014215221509711455768065495002 |
|
169 |
16.2936569977 |
-19663326824278379.781915458664274789259647484755849 |
|
171 |
17.8511725008 |
-709859666626589186.89887967948307722229532245827653 |
|
173 |
16.9969450639 |
99299043218361067.296880530097313145555707279521159 |
|
175 |
19.1552559738 |
14297363988543687791.569487400306999077248732113220 |
|
177 |
18.5710286081 |
3724162374458363938.6025087220637493882297078589556 |
|
179 |
20.4762786179 |
-299418491442947779873.89414842802170101063633041217 |
|
181 |
20.3030672637 |
-200940400589469064857.06672669041518076622328211713 |
|
183 |
21.8139725125 |
6515871523484110776757.4571447302223398243488406593 |
|
185 |
21.8545964051 |
7154781989226937259657.8901140215885417931463072149 |
|
187 |
23.1680286265 |
-147240955300617535666506.29084502328265877891859819 |
|
189 |
23.3576729912 |
-227862569890152577146432.31557452042629506678490852 |
|
191 |
24.5381026149 |
3452252993788977551697568.2171662109438794112556586 |
|
193 |
24.8448072715 |
6995314933293117259417262.4132443792680504535241877 |
|
195 |
25.9238172189 |
-83910675820472901511224368.686269694286019981232784 |
|
197 |
26.3289815407 |
-213295425208998889529452639.91955973445403987822490 |
|
199 |
27.3247617063 |
2112329704503563261045436899.1249461748213185179015 |
|
201 |
27.8166007785 |
6555423874651256623811186991.5127246472613403282088 |
|
203 |
28.7404883854 |
-55015920704231595201655700531.934344786506767283513 |
|
205 |
29.3112243009 |
-204750184108111036318372156451.01448093719901635310 |
|
207 |
30.1705058289 |
1480832130259152649116847744121.8274053013605879180 |
|
209 |
30.8149798111 |
6531001914618260804220422825294.3576812759110857483 |
|
211 |
31.6142679639 |
-41140348269701921039776038858282.156735823224590020 |
|
213 |
32.3291975543 |
-213401542507044909517183478237930.12686236360251112 |
|
215 |
33.0711574917 |
1178033095747560447910133881462946.8682069396044942 |
|
217 |
33.8547296966 |
7156978236497201747578200596810785.8792596988110275 |
|
219 |
34.5404609981 |
-34710510268694446652138947473193192.265430546671744 |
|
221 |
35.3921254941 |
-246675202918808974522416971048901647.66040883526662 |
|
223 |
36.0213311891 |
1050343105607514379829575964244169432.0020968727508 |
|
225 |
36.9417338711 |
8744477630136331873475548462079598452.3740338503341 |
|
227 |
37.5127281510 |
-32563280558350203048329359979221817098.289244696254 |
|
229 |
38.5037666846 |
-318982373062494632138590932148270824819.21492173750 |
|
231 |
39.0133245837 |
1031156499802639798508740828281832319124.7425544789 |
|
233 |
40.0783394143 |
11976761857776164882333840018786711471182.781575758 |
|
235 |
40.5213453496 |
-33215848390405965670602978367005753094867.423202064 |
|
237 |
41.6654982476 |
-462911795898660646034286983710811207377114.70134202 |
|
239 |
42.0342783457 |
1082127280438054226869476092745191210364608.3463164 |
|
241 |
43.2652386323 |
18417837306222347682123739412093561214921141.605294 |
|
243 |
43.5483092935 |
-35343478744179715837623756314632663945862794.245619 |
|
245 |
44.8775182869 |
-754255154718214608603078672188602412199619751.61642 |
|
247 |
45.0570881838 |
1140481339624238167769469726343452954284707197.7127 |
|
249 |
46.5022665050 |
31788241593699064721718864590717030478171478153.304 |
|
251 |
46.5485763701 |
-35365220492708296140377087748804440170254492009.570 |
|
253 |
48.1393909147 |
-1378449672866233726070664896135098313484573633108.4 |
|
255 |
47.9946901788 |
987848122496441964413343332623221752473112662017.00 |