Rule: Q[1, 4, 12, 18]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^5-\frac{10}{9}\cdot t^3+\frac{5}{21}\cdot t$
• $P_3$:
  $t^{17}-\frac{8857204}{2038671}\cdot t^{15}+\frac{28927370}{3714291}\cdot t^{13}-\frac{6039926464}{813429729}\cdot t^{11}+\frac{9865688404}{2440289187}\cdot t^9-\frac{11887949788}{9490013505}\cdot t^7+\frac{122410578862}{592447985955}\cdot t^5-\frac{5464102072}{355468791573}\cdot t^3+\frac{39745277}{118489597191}\cdot t$
• $P_4$:
  $t^{35}-\frac{76268206239072074059187307411020211950692178101858193961865245497528777591161027999437304748780311435}{8300604736320144452778462999646683776984367516037275033077875094241987391129945575067206054358877997}\cdot t^{33}+\frac{22727897642518781812900020776152671330003360639605405780186675924124191550911311670709637766308755105230}{587833735417581138974038425156796969297347481363003386433424063492228016153657054816123046940505996333}\cdot t^{31}-\frac{6439947286613854183712200949633679832505146165928848001620728487301067639694937200355340367455965010819778}{65249544631351506426118265192404463592005570431293375894110071047637309793055933084589658210396165592963}\cdot t^{29}+\frac{733774265698104418678951214441679434023866539235131218836609755399599733734148331497839469840378522012193026}{4299719992776300992424551889058101031873194658420746252884287785242582724638961659470718511726450774074217}\cdot t^{27}-\frac{168289047238244987042121283422596880353145831349546879462209691692482504393694373835378516466209319694442438}{796244443106722406004546646121870561457999010818656713497090330600478282340548455457540465134527921124855}\cdot t^{25}+\frac{1646515207564512742721527919273773338721670831857623700972312912806662837841218281406142570356269968011451436630}{8516961311161254877777894353987916610049516896228538418815100044393888214277940045855350562656735755949454789}\cdot t^{23}-\frac{550116762082577219463953482001149105730628727760721718075661718985763613750166589755370990423269338010552044046010}{4144797737209909819433390065399423939838445331282001327034670208560903947061434040576475602078993187667054237099}\cdot t^{21}+\frac{8299306691896459266973778220176571326871085284237755986995415032852124952942139443891149018314065692338975431557460}{120593877020726423793990539521859429868632861781585848134199214163367252935930295180582218708107849412598578041309}\cdot t^{19}-\frac{2105908201643977513603026913548082278912303777819362538426563696317272963785855792602159194355491917464279563160280}{78280235960822415445221929163312261493673962910853971595883700421834883484726682836518282319298077688879778728569}\cdot t^{17}+\frac{5533146427896403728174826322925727913689308296571764191228536267033656853074663555286446758728121737088473881040658}{704522123647401739006997362469810353443065666197685744362953303796513951362540145528664540873682699199918008557121}\cdot t^{15}-\frac{1448518330058432336915942590932019314676939846371121739885777066059900179264430685489844302341580585231772680665190}{861082595569046569897441220796434876430413592019393687554720704640183718331993511201701105512278854577677566014259}\cdot t^{13}+\frac{1989758211874725975740812216917317743559868022096160090268677323164531073749665359097014208106521516328302279770}{7742001358762656472604366620547366521352369958216326861131354986774878586401540060754555394216293397801296797331}\cdot t^{11}-\frac{2386976306890085171315345939436867413741534652197705533549509605570978583460274126240634357284309590851332209690}{88959977877102977204076590036100871915162137821768736951490475225394359606010148999991023303353258099263957539143}\cdot t^9+\frac{6571390326472991128800515981650181964678271329352877673055478927277024397215406517834158795495378210883179140130}{3667127976933911615856934989265935942280572570208466823222551812069034157092196142110741071727117639425214249669117}\cdot t^7-\frac{180126447489698820918213807616776152791866784666153772364169764742300658780374084714720734961081580765497121302}{2619377126381365439897810706618525673057551835863190588016108437192167255065854387221957908376512599589438749763655}\cdot t^5+\frac{1960123576426401638946220490579720109073507901432202151665792626523452284384278868916889983772902842723666843}{1571626275828819263938686423971115403834531101517914352809665062315300353039512632333174745025907559753663249858193}\cdot t^3-\frac{1993915088600883915032944028824345043332850700916128370123640119731806274159433379060546915707186554863861}{293881336130592220086095835376712636489383864511479919631075580758145594470803175151731862891023364831985810949093}\cdot t$

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.