Rule: Q[4, 10, 28]

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.

• $P_1$:
  $\frac{35}{8}\cdot t^4-\frac{15}{4}\cdot t^2+\frac{3}{8}$
• $P_2$:
  $\frac{35}{8}\cdot t^{14}-\frac{436215}{27784}\cdot t^{12}+\frac{12954799}{583464}\cdot t^{10}-\frac{3039465}{194488}\cdot t^8+\frac{2679105}{472328}\cdot t^6-\frac{8846695}{8974232}\cdot t^4+\frac{1485}{22952}\cdot t^2-\frac{273}{390184}$
• $P_3$:
  $\frac{35}{8}\cdot t^{42}-\frac{5897514933563278719248070870019895061181879123589638214796321316131851476496857260020350854916463}{125199979520452898815527663841304356123642327278854720506671177078723754504560141028220283839258}\cdot t^{40}+\frac{36284869084215859101759990752921491885476421620854398147466835552842174299384921300768329139897682714551}{153960668415932297825633047723601110203653195416698669192022666534894017941838687504940991002244669244}\cdot t^{38}-\frac{2455705785604648703958141699923416549823453014759340576687777545119064910476817752624609644260949627567}{3376330447717813548807742274640375223764324460892514675263654967870482849601725603178530504435190115}\cdot t^{36}+\frac{183001714746325921420363228651302009181609091732927042151721691853432320386853805415299099701445813354719}{118075099085902965249733615547423407825358089718069656072077533733527743083214632522586323926533505736}\cdot t^{34}-\frac{209317012876074734853716931863905188590883069939683418241126303375032707809684150466699421027120415323253387}{86536892840355089399279032324072652585181928195285844848001883068791501941737759426884332728333093020074}\cdot t^{32}+\frac{2435127789378980252400166501988968703408189651839030817720749533268967129610961797067352345431269290777893903}{850946112930158379092910484520047750420955627253644141005351850176449769093754634364362605161942081364061}\cdot t^{30}-\frac{16580738870462665762619678074079123422712083121636230072145588428022738807845940912727493699736825542564924252}{6326599361350307948908160558822963709651452706972745570083268103485778718044871412013304586204004170141497}\cdot t^{28}+\frac{463941985942361304344727704159334746277138775462849751556751972586046493877505987739987368284513188364656623}{246651047226132863505191444788419637803175544131491055363870101500420222925725980975177566713606400395380}\cdot t^{26}-\frac{1745840225991843763308106257949747107279939871179835188072920948372378678503959850271286626008763889002541815}{1640229464053783542309523107842990591391117368474415518169736174977794482456077773484930818645482562629277}\cdot t^{24}+\frac{79535630172927338513395521034579966517852835033696124789669526214125982175076477565603998177521535774870948285}{167303405333485921315571356999985040321893971584390382853313089847735037210519932895462943501839221388186254}\cdot t^{22}-\frac{665296334020597593246089537353520768724120574409755387410400367963079339306158142672347993907796714117293290}{3983414412702045745608841833332977150521285037723580544126502139231786600250474592749117702424743366385387}\cdot t^{20}+\frac{1804714080771948005437979206345992646619057022348567643834313009259293025021636219431196655688303356655450605}{39414837346736031588129592877189458120947451952212270647146442219767151623531011759833375160834302783181724}\cdot t^{18}-\frac{91875781665198014046367725087143612067473205863549420667246669698464575451968298464808518341242675408089}{9502130507892003757986883528734199161269877519819737378772044893868647932384525496584709537327459687363}\cdot t^{16}+\frac{6114661611646307022427249756134093547776522355189563885200305303250228068291155989847789425098230997996779985}{3962930043229915411294735683843298899601731308783460211978532727302176700736493050029129205509178354832550691}\cdot t^{14}-\frac{1674473754395300524987006084568986749100756138949058706786442969539629357849718792941522120001202451919311780}{9246836767536469293021049928967697432404039720494740494616576363705078968385150450067968146188082827942618279}\cdot t^{12}+\frac{70086459170907682381503950005174990420009258289673318971517411863078275260976235948400032593156925822586741775}{4660405730838380523682609164199719505931636019129349209286754487307359800066115826834255945678793745283079612616}\cdot t^{10}-\frac{108153408332742375418670218514817357540917367022819091596908046644924623296459132547137280594221705071418815}{129455714745510570102294699005547764053656556086926366924632069091871105557392106300951554046633159591196655906}\cdot t^8+\frac{8041908160832601560073454943702580150479535029591806199964088865442919859704625802604107698956548903557}{282346160840808222687665646686036562821497396045640931133330575990994777660615280918105897593529246654736436}\cdot t^6-\frac{752889440435853396522931414844920437182129830531113256059042728397965239504545127465225446142984296115}{1460026858032074098898060515100162752484848376920222183360512057427117731850286913168626549398118341254097623}\cdot t^4+\frac{11965238891908756382254146602913433085345044663943937124410189996964525371036540097736816204868098115}{3216291049577902362789930410075720846053579033215561911170983083027853554220921895675815007369767940153954184}\cdot t^2-\frac{8744109359232478852283715970356137819847354047008444179035978570950643709438743027530373185242925}{1952748137243726434551029177545973370818244413023734017496668300409768229348416865231744825903073392236329326}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Legendre type can be downloaded here packed into a single file.