Rule: Q[1, 30, 32]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{31}-\frac{465}{61}\cdot t^{29}+\frac{94395}{3599}\cdot t^{27}-\frac{3681405}{68381}\cdot t^{25}+\frac{55221075}{752191}\cdot t^{23}-\frac{254016945}{3624193}\cdot t^{21}+\frac{2963531025}{61611281}\cdot t^{19}-\frac{544322025}{22698893}\cdot t^{17}+\frac{544322025}{62755763}\cdot t^{15}-\frac{20160075}{8965109}\cdot t^{13}+\frac{157248585}{385499687}\cdot t^{11}-\frac{786242925}{15805487167}\cdot t^9+\frac{60480225}{15805487167}\cdot t^7-\frac{97698825}{584803025179}\cdot t^5+\frac{13956975}{4093621176253}\cdot t^3-\frac{930465}{45029832938783}\cdot t$
• $P_3$:
  $t^{63}-\frac{62433}{3965}\cdot t^{61}+\frac{1971860877}{16701425}\cdot t^{59}-\frac{4510836030183}{8040745375}\cdot t^{57}+\frac{2729757154081992867}{1439401337391875}\cdot t^{55}-\frac{159746877204889147222329}{32907985939454153125}\cdot t^{53}+\frac{10337250824100938199456049713}{1057280811276079796453125}\cdot t^{51}-\frac{449833894656241368285292311819}{28297809948859782787421875}\cdot t^{49}+\frac{98569096924696187964544498477911351741}{4641156817086526180697413047265625}\cdot t^{47}-\frac{31374484229921027547943195239820105166113}{1328654573912749143857099841509765625}\cdot t^{45}+\frac{3693274061266804916628060096281026527739675070059}{167504756903429810853715377692150756435546875}\cdot t^{43}-\frac{180631122886827664038688893695168188427581152648949}{10381399468549777812212825152315855020947265625}\cdot t^{41}+\frac{1825682811303346590929613613943349300013307078400670795769}{156662712828501000753633133391338286035506110595703125}\cdot t^{39}-\frac{74229168092236183372216113892584238479911680641942323456308867}{11177623455792165568770468012249667811489968480819091796875}\cdot t^{37}+\frac{4240057362429851127184279444565450137817484332585925591488712941}{1315636490539861650053929410631008197811859803620733642578125}\cdot t^{35}-\frac{2475308844063590615669546738874739591651915241906020751977871953739879}{1859295875039928615262584869778316791146403266082483388641357421875}\cdot t^{33}+\frac{50803406020041547255798654716446361008056056525329783244009885763546450130893}{108726462099435804745964600261570894887863328006347361141504684906005859375}\cdot t^{31}-\frac{97424445122425825737771594247340618770026316197643043582893719167126994979}{701461045802811643522352259752070289599118245202241039622610870361328125}\cdot t^{29}+\frac{154036152645660659772881359002695554630379126545742607166500400208629726481}{4426461082134983819468636673607891827470297892138279663825441009521484375}\cdot t^{27}-\frac{2126393768287681496323136862127020245215805915436312839090139210262457007}{291149614098064710533611553782458882743308334042540133963992218017578125}\cdot t^{25}+\frac{32406979339271291566682114786188015259423835564996372933971978658328236279}{25446476272170855700637649800586906351765148395318007708452919854736328125}\cdot t^{23}-\frac{1010167254423523217275415408317467518715425906294748857763289731955818009}{5531842667863229500138619521866718772122858346808262545315852142333984375}\cdot t^{21}+\frac{1246156371939261336650953115810368715418732457882533100165332390818421729}{58637532279350232701469366931787218984502298476167582980348032708740234375}\cdot t^{19}-\frac{103594520217021197264403537865786335430620067169979230972798703233655039}{52465160460471260838156801991599090670344161794465732140311397686767578125}\cdot t^{17}+\frac{3098201093221736882472630129782409636004745700990512263967453404812669}{21603301366076401521593977290658449099553478385956477940128222576904296875}\cdot t^{15}-\frac{1149306231713351259707130645819940893995964297536075033971516278436761}{145050737743655838787845276094421015382716212019993494740860923016357421875}\cdot t^{13}+\frac{197076704957270155690432408484270092373911299705607843514295976935699}{613676198146236241025499245014858142003799358546126323903642366607666015625}\cdot t^{11}-\frac{189483052455767447452638362894519760396667568500799288806552999149}{20860139541729769457783768802876600874437448551370301919254246453857421875}\cdot t^9+\frac{6943723334223740871719244562974629277603225629292527507522756671803}{41629561732429225732111594239098831414839552849738132990627084905694580078125}\cdot t^7-\frac{111387054316412410968669251278973342559819436407999202893288898227}{62724865251827323946766526090717646255782506854457186905014933860601806640625}\cdot t^5+\frac{25649265831582211792106216161230401901761777159686244357511035193}{2860545599042636796735096689858076844362546417246291709784518262805584716796875}\cdot t^3-\frac{58358515889653926251524930386245780070105416927209292345751813717}{4305121126559168379086320518236405650765632357955669023225699985522404998779296875}\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.