Rule: Q[1, 2, 8, 44]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{5}\cdot t$
• $P_3$:
  $t^{11}-\frac{10483}{3705}\cdot t^9+\frac{3234}{1105}\cdot t^7-\frac{139986}{104975}\cdot t^5+\frac{68299}{272935}\cdot t^3-\frac{3633}{272935}\cdot t$
• $P_4$:
  $t^{55}-\frac{48106547474891507491668710569229085124182174818121116041098367735045002141826423630832330137555103453161796171}{3399603140566430159157283133047599304039034599212289203073015362616128898173321488149101500502720497028090435}\cdot t^{53}+\frac{23218537280159990477645402725921220597057911000296764564710959985817972836359294401014495368192138425679092025783471631}{245086334759296780451397283873324482061942930957244456182426962594415775304445840089504047457288943288382720365084485}\cdot t^{51}-\frac{7819848422076128915963282283894179469266061360038271275914922221956273970127300891507371995112296444238543978913993780059}{19594412183285425345343672260099867512928747189903304816435837201617076122085244478057721629457841909099053019933244689}\cdot t^{49}+\frac{18022968719232518198134738460188888638296329273578937782085450280733243835299055945586950646241839387846244677261608741233266}{15185669442046204642641346001577397322519779072175061232737773831253233994616064470494734262829827479551766090448264633975}\cdot t^{47}-\frac{23540652412299968880175769109457273825019956985073882697678008170993428306590895354317747983795199019285952228872767228729811954}{8883616623597029715945187410922777433674070757222410821151597691283141886850397715239419543755449075537783162912234810875375}\cdot t^{45}+\frac{910466819827349401403023810461331310148499521298298360184213784679853730179283696936507618875290723415335123642971563141125702}{197413702746600660354337498020506165192757127938275796025591059806292041930008838116431545416787757234172959175827440241675}\cdot t^{43}-\frac{3267457298327011655031124872078086216492398756375546934555701236024951210190741896368221496609680899755801542837187116280776131854}{509524766788976304374545082390926412362506147208689829542050525360039760221352811178509818720729201421400407632810623263763175}\cdot t^{41}+\frac{188224061322117237534601166684272961840751491877200935426311074649638664213235892824934610046533870831287122188824231583752299118311}{25985763106237791523101799201937247030487813507643181306644576793362027771288993370104000754757189272491420789273341786451921925}\cdot t^{39}-\frac{528812859031953390899509210045780489190360837933787507199583466853567392710238879103938525825986323497187014454254601428189592933}{78667189620226016574295121047554127130265474746849912406590796726448856731844711300238248628400142598270705237979624622515575}\cdot t^{37}+\frac{18282370789670376806177641508850257521531375701376353945932999562070454738807066339540472712810467943419217915163699963928283709683}{3540023532910170745843280447139935720861946363608246058296585852690198552933012008510721188278006416922181735709083108013200875}\cdot t^{35}-\frac{32570210927174714055230339758400706434119509891036916895843734161808124072001277992933175120511871929074989819862942859916128551043}{9870418556467181961939499599672526656991544566766521362544598201030318318177927600200481430845735538947730251330031724695630675}\cdot t^{33}+\frac{20721648363456199829792316665240825072613551275831972689407395361730586411680561133957988385516302347383064585542563037148320908}{11792614762804279524419951731986292302259909876662510588464275031099543988265146475747289642587497657046272701708520579086775}\cdot t^{31}-\frac{14270238539603465765531065259852560876409609261715217918428060510549000524691612847867234929174839187561056602426671814446117356}{18298884976765261330996476825495970813851584291372861257961806082740671705928675565814759790221979123002836950927014691686375}\cdot t^{29}+\frac{692136001216003399963549796079253681015410985008318828785880771073850039880993601067409701219656719596434515122322361801106398436}{2404473485946955338892937054870170564940098175886393969296181319272124262159027969348059436435168056762572775351809730487589675}\cdot t^{27}-\frac{190573389861325144697492980739641753661754135908446104878830319176174681733494723258884964182050121837345907849718095306685516948}{2165368055583889257501249757683689879639104141145788582192147053124312818534893275288079908509600862888669039193030071849554375}\cdot t^{25}+\frac{140047119960120091028162730849831964665328413748115261317020138698051149668391372294972743730921758887544486078442007998908619457}{6322874722304956631903649292436374448546184092145702660001069395122993430121888363841193332848034519634913594443647809800698775}\cdot t^{23}-\frac{5780688133532986498226070485693904503539350822476109761285790729225032971499507182443414536865558683030063762051219968361516243489}{1270897819183296283012633507779711264157783002521286234660214948419721679454499561132079859902454938446617632483173209769940453775}\cdot t^{21}+\frac{4148966964485409178281925662231514609969783733287870267755886432621014637639146978652312386159736313157275092383635170920949772677}{5507223883127617226388078533712082144683726344258907016860931443152127277636164764905679392910638066602009740760417242336408633025}\cdot t^{19}-\frac{162804407892139703561473239103953390955027222414750868774933157924043468979636236724418036891946721177446801729169524923438540437}{1642505368652096365764865527598340288765321892147393320818172535676950240698505280761342976832997318109371326191703388065244680025}\cdot t^{17}+\frac{897762004782840131016618972032230903397455114175750209965668560361235945374378870110271045268639337145737289481370209683434792378}{88405436018627539686755997514851844954133501842050875796978110008494674719948960699801695517776032121769103733259329416452875424875}\cdot t^{15}-\frac{539383517038721124672572429311336162670296836761879788159667590784601964872969733837201485082201008430345610300498317640992524938}{683465474323320496474851539407923573748852796999579529437327319444982968007329551341225521899496082817263208861956608798921885181275}\cdot t^{13}+\frac{144549311933678682012970030155836994745823872283154313302233505676097098627025101025748695224939666173831139482556181884541134898}{3218713473095295671432847847980905035347161462792891630085191051403295857880671647769361218518139672071042975067846935454751784058825}\cdot t^{11}-\frac{464552326386964513408059810987682129424554680019452139892059544091642814258502137933092921856042865466796219977298003778721676546}{260715791320718949386060675686453307863120078486224222036900475163666964488334403469318258699969313437754480980495601771834894508764825}\cdot t^9+\frac{1329531183226440067260743266512565884452845715919381141023552501792945686219556854592271552797118080434483145247882924012033101}{28968421257857661042895630631828145318124453165136024670766719462629662720926044829924250966663257048639386775610622419092766056529425}\cdot t^7-\frac{1689126886923769928511713872406929402786972751267496985707088644995265951037495678179745524408817876218668259514154267447996201}{2462315806917901188646128603705392352040578519036562097015171154323521331278713810543561332166376849134347875926902905622885114805001125}\cdot t^5+\frac{7196638623708693894664964252216353957025472484475841064075662110529714641925888231800346762838878005225557927629431355386269}{1477389484150740713187677162223235411224347111421937258209102692594112798767228286326136799299826109480608725556141743373731068883000675}\cdot t^3-\frac{76317189770530784003588676915963997969687603439154026431541653380119550986931296359986294036140248042318206323469407693}{7350196438560899070585458518523559259822622444885259991090063147234392033667802419533018901989184624281635450528068374993686909865675}\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.