Rule: Q[1, 12, 40]

Type

Polynomials

One starts from the polynomial $P_1$ and extends one by one with $P_{\mathrm{i}}$ until the final polynomial defining this rule is reached.
Note: Polynomials might be truncated due to size! The complete polynomials are included in the download.

• $P_1$:
  $t$
• $P_2$:
  $t^{13}-\frac{78}{25}\cdot t^{11}+\frac{429}{115}\cdot t^9-\frac{1716}{805}\cdot t^7+\frac{1287}{2185}\cdot t^5-\frac{2574}{37145}\cdot t^3+\frac{429}{185725}\cdot t$
• $P_3$:
  $t^{53}-\frac{2474311509266680302092501370355455140919906488404227293366234543440867137382}{190606786497466028261714696484921107816137633214151821999201192945955876725}\cdot t^{51}+\frac{25484557085760472691390483406752628256523863632412514803611299124037346906864019}{320730227503556136435422085481247049700058472656788987841615863346301034647623}\cdot t^{49}-\frac{76824043088356799631132696219180571478149029606804845574584792185756740072172298712}{251940566100293422477337861669116975953519844586530723623237991438157425781678467}\cdot t^{47}+\frac{114233116544108225255679957646083177651946329421061617788703859571550570930510850229342}{138819251921261675785013161779683453750389434367178428716404133282424741605704835317}\cdot t^{45}-\frac{3917952728077242911679866953083529657006323161599275230802411237094482979900207631906172}{2359927282661448488345223750254618713756620384242033288178870265801220607296982200389}\cdot t^{43}+\frac{2547928849654780346427296532357498109503887471307368315938322601931711039604415081012004794786}{980349192126805623785931124212022432975206456919904258408825391467814058580275860774596435}\cdot t^{41}-\frac{634143316711014728257745666792763923617829377166258303891396202867670868251289647781524858424}{196069838425361124757186224842404486595041291383980851681765078293562811716055172154919287}\cdot t^{39}+\frac{7031429438369912929652084448825625780423758672362798813804237452779006087647176337502491889}{2162434348122787778279730805884399614827343573828631478830021106406737697273259611927771}\cdot t^{37}-\frac{116024392312993552314606014122913132527574035409321748801590504869774671542245892302178106364118}{43458443094223665980087750005858779059185123803234006830046934175456207502100698420912413787}\cdot t^{35}+\frac{658299762024699631083578623754377746648632739783466600971346386051847262957134079340961649195}{365197000791795512437712184923183017304076670615411822101234740970220231110089902696742973}\cdot t^{33}-\frac{8727343245136275757925945849361912988948086137704094110172891262099393049387208249176738960}{8686667011339547868345711795175092949885173331679720760309591427444143652993340794024841}\cdot t^{31}+\frac{29529079498568783549276725332861769084846138751966215064090775767633891686618985735308419940}{63802071497080127446815055599044648218122135160268293860204930139503537865089020314734177}\cdot t^{29}-\frac{258314211670948965196425963787410443679830008160718026092689879228645383850948703620230624600}{1467447644432842931276746278778026909016809108686170758784713393208581370897047467238886071}\cdot t^{27}+\frac{26948421310885932158735815441155198614467936272053425432416829222367362618875221178236858580}{489149214810947643758915426259342303005603036228723586261571131069527123632349155746295357}\cdot t^{25}-\frac{6901067661026537530510256564543514547349158688563748688326396180494976394256328297128575632}{489149214810947643758915426259342303005603036228723586261571131069527123632349155746295357}\cdot t^{23}+\frac{198407086155910249587671213597268941178080436029263966151570894956200077381700111851901701}{67668863709024377595106877150501899625281052442708796518399168329776479553882294273202915}\cdot t^{21}-\frac{634408034577536599916715752581569248873522695562814733741910158320531335852193929662884366}{1297308787107295924751906130513907847101816748258788641824166912836571936590143413066261599}\cdot t^{19}+\frac{14810180711082206410612904395394126226194353125611511017492439939917447145778160432135196989}{229623655317991378681087385100961688937021564441805589602877543572073232776455384112728303023}\cdot t^{17}-\frac{19697072497477274126533752102347705224594549630209419043971828307893744945803788096884812792}{2985107519133887922854136006312501956181280337743472664837408066436952026093919993465467939299}\cdot t^{15}+\frac{374370750976966452070879783647188133414314536145703606752018025768626593471666068579211830294}{733341413867225133047832745550771313901867869638979784661723248321344547743739678394683290421121}\cdot t^{13}-\frac{8143261504066343289434465674914237534964641724639777406572717005394591340712128625812932652}{282054389948932743479935671365681274577641488322684532562201249354363287593746030151801265546585}\cdot t^{11}+\frac{99300868421188319401254316187832928295421100869903224199731328336885980089798428383634714}{87180447802397393439252843876665121233089187299738855519225840709530470710794227501465845714399}\cdot t^9-\frac{2377639344951443220431617567667329765641281941575379133295681055533472185253927738511745288}{81164996904031973291944397649175227868006033376056874488399257700572868231749425803864702360105469}\cdot t^7+\frac{2235055162637911970446843304083103991158416167310064266216937808464512916252803093789}{5061108493111677576351212673765369325185884727571046610238776435778067483428909758924032073337}\cdot t^5-\frac{859976229593837252547194411847556220524768550321209807358975771815842818252950094733638}{266684989827533626530674449418718605852019823949901159033311846730453709904319541926984022040346541}\cdot t^3+\frac{2116969384427911763649821575353654194521466692201543516845470633135781256939491278067}{289874988942971333185515705889911528100021547771631694601425920359188815113390806442373937000376675}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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