Rule: Q[3, 36]

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.

• $P_1$:
  $\frac{-1}{6}\cdot t^3+\frac{3}{2}\cdot t^2-3\cdot t+1$
• $P_2$:
  $\frac{-1}{6}\cdot t^{39}+\frac{2826124439249230977594611138180103316477719078386626737431899418184513462500496266212102857216549}{11734507821847426871684955250532849654174290232309975346819395579408550305377492447627422576014}\cdot t^{38}-\frac{56949171817099171550765347923415102737306949460213461676300255985263042124797105174241686679055641}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^{37}+\frac{4605896007077422204609839449778206760104851359327214958013648566128893970529699020848726003412714160849}{64539793020160847794267253877930673097958596277704864407506675686747026679576208461950824168077}\cdot t^{36}-\frac{1412540924072984356091356923275332519698402898035789743967357297423657507382601451260345921436537987947124}{64539793020160847794267253877930673097958596277704864407506675686747026679576208461950824168077}\cdot t^{35}+\frac{327129749722815659498260963758268462735219797244662609672317650640351909339862902341405084510795250279274660}{64539793020160847794267253877930673097958596277704864407506675686747026679576208461950824168077}\cdot t^{34}-\frac{3499545176858990349745841392767315851698708861554668677655996588846649567095437373833217773069821885667460280}{3796458412950638105545132581054745476350505663394403788676863275691001569386835791879460245181}\cdot t^{33}+\frac{46647819039849965462501200253510040637478972210743521156652447745770486388337555562703247467774907038917669080}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^{32}-\frac{5618725306498427892722211117759053281941040192554659608663430065221009059321840429166246415268248735996764994560}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^{31}+\frac{563626701537856633467689432910332890139675939567113834462812754715960636563040578614930511300290257952437492136960}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^{30}-\frac{47571060847095049519584966506068098733978178454325509695136851527166145924207644131119017299883083631736966741964800}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^{29}+\frac{3404450272369270094077751318989312980148174845695174221143171518000567403400170163739821236814672952171169931675084800}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^{28}-\frac{207791270867719344309290118984500792897007940774766102728791091385971809382212905907799507542692868074184443720378572800}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^{27}+\frac{10863009442988516843383110108262804039670766532505521458588928764336035130221865657802637016614850903367215198084359577600}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^{26}-\frac{487915745165674512830336182446925542822870833330120874288543230467247426055218930822715004373007614173132657356073558425600}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^{25}+\frac{18866277437396967333110070443717040218968415373701429188256589309438575917025680147585680738475343590566364584570570700800000}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^{24}-\frac{628712177114176034826755919974155984639540280092463998988643788479487344918191624727774425661754763742158941445071300812800000}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^{23}+\frac{18061771395976412130411883055717597798370984096775489351563549429600219873202162191438021319211892900709217006808547084492800000}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^{22}-\frac{447090114206940963446335849672069365968045030222910922938273795073378609877654836274843369895868689743075098785907535753625600000}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^{21}+\frac{9523939603335351132203194094611447196047990344932861086960763092404842496582074040289118872596358355356174456397733649031577600000}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^{20}-\frac{174246820171488081377842519019764253573461675877996087897037209999573748256320642075902531675737747141436824599775135603236864000000}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^{19}+\frac{2730558365962499664942329262560357268552765414520106307735511815154194787901775174424964395346105006689125585130258476037545984000000}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^{18}-\frac{36521044822939718548828083943117763526334871593534688782759620802377365132490665658945400551874451747663814765699458253260242944000000}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^{17}+\frac{415082844389296651193946220741284088399861954170123709823792447714738210411048041615335828873634394666016078098425760801884028928000000}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^{16}-\frac{3987587156441772704568108584459734758925143302885346671807989733389469823376899193260072692964421434496567301842318317343049515008000000}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^{15}+\frac{32172862510797161961909963461115989298518278743039078989891378195286575633332507139816476409604068951135242292446677733942117269504000000}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^{14}-\frac{216351196801290956482075246972904828329286879142873204767273850600873785910400130987354844437473967938969675713783357854938781712384000000}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^{13}+\frac{1201646412888744675545571844186381762533713466277862821239257692158940630647484773653802590380671960399401519074124754414558174511104000000}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^{12}-\frac{5453129915187879354935752287625808980410974146815146029211466522669770977029629136765264340443094750489079414402551717595806106124288000000}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^{11}+\frac{19959390312750066878023025728253362454758599448897402383123964018635134468483684150864407642597615958530992902730304486576245794930688000000}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^{10}-\frac{58010152796205916109599977201953647386897411921600134529865921978954196509637458930335900556886885284545958234415675240773328799006720000000}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^9+\frac{131356016772862331443243010452501545118178164742569086437273156301740272677075216283245933505183804656777468537663826713263725262929920000000}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^8-\frac{226330351661025224282825195717510528736483573201917598731052074433167004834890178637041725917149336302766439934519167793437358759608320000000}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^7+\frac{288014317562481098645690625609231719906722077970795920670674465230174995656887581927479901270037575155466653167668517804282971674378240000000}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^6-\frac{260341713322024410382730705758091387551738684504665430088589627787960719518141221080815254085754913168732301953207940394058931597475840000000}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^5+\frac{158524629455956175107630422845708739129605151249078155966785334300717496985858704893873751431854767453726355082725559514710366434099200000000}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^4-\frac{60215271607010495393469306315272186573413845353207074973711749903347649067199793021753147952549281983432394905654405519721763124019200000000}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^3+\frac{12626722151642545711173099073123496759095449553175187196293733393562511315117870384806503029470148313125106785273996774665796924211200000000}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t^2-\frac{1165549975321403577502103676545664356493987174712726869256423986257466225203796985545377887063637778542113832720015943859102443110400000000}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}\cdot t+\frac{26938192192129074356924762808239527653341648944840390690725095424354625170961743841950319672718158274435506346148119323137697382400000000}{345132582995512555049557507368613225122773242126763980788805752335545597216985071989041840471}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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