Rule: Q[1, 3, 21]

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.

• $P_1$:
  $-t+1$
• $P_2$:
  $-t^4+\frac{49}{4}\cdot t^3-\frac{153}{4}\cdot t^2+\frac{57}{2}\cdot t-\frac{3}{2}$
• $P_3$:
  $-t^{25}+\frac{153017369601578761787736776779247597348907940012457474030335047284332052239}{273434064559078089777878564374650933851057879499729097485061779728549636}\cdot t^{24}-\frac{45556795638842989400661455487811565788965413491449478620587663972279835724345}{316607864226300946058596232433806344459119649947054744456387323896215368}\cdot t^{23}+\frac{135848276910169885325756520103135459265883250248532868581242570898710045585118889}{6015549420299717975113328416242320544723273348994040144671359154028091992}\cdot t^{22}-\frac{7291119661429743974753341754749883663749393952074545479551742679864173750928270267}{3007774710149858987556664208121160272361636674497020072335679577014045996}\cdot t^{21}+\frac{568483555771405471256016858378967307530474451080065896952824837183321230334334483987}{3007774710149858987556664208121160272361636674497020072335679577014045996}\cdot t^{20}-\frac{8344070772096184932410717706545936069822408380651240488052809378421145084309013690945}{751943677537464746889166052030290068090409168624255018083919894253511499}\cdot t^{19}+\frac{19864256289474111745612716306370433447948309897485507292397616284885552451301957010525}{39575983028287618257324529054225793057389956243381843057048415487026921}\cdot t^{18}-\frac{702502892109623653759744671461776098737292158861062558169675576040913865530254726807690}{39575983028287618257324529054225793057389956243381843057048415487026921}\cdot t^{17}+\frac{19603881924039445713877754614344986912073458150540414431894005795445226668831481777292690}{39575983028287618257324529054225793057389956243381843057048415487026921}\cdot t^{16}-\frac{433864066139538936496966961604160875190723551486831516801569119793322218891073590279797440}{39575983028287618257324529054225793057389956243381843057048415487026921}\cdot t^{15}+\frac{7628537569595419639293130715845921391793075332659564691899115450875524533210160055269595200}{39575983028287618257324529054225793057389956243381843057048415487026921}\cdot t^{14}-\frac{106441514896651449774398984290205452274631450410840344859381130741854624402058320467212720000}{39575983028287618257324529054225793057389956243381843057048415487026921}\cdot t^{13}+\frac{1174080971744547798581746279502646181206476883349031015443000877156159307527719118020085577600}{39575983028287618257324529054225793057389956243381843057048415487026921}\cdot t^{12}-\frac{10171027879683504015475437170893288132711247917278216852513530669096853837383915696463086169600}{39575983028287618257324529054225793057389956243381843057048415487026921}\cdot t^{11}+\frac{6232084722940353659254886886348757881336657866846137415129607659597646288059816749476122457600}{3597816638935238023393139004929617550671814203943803914277128680638811}\cdot t^{10}-\frac{32270299257637621397306370379096667034905489601604376819198939863876649258824284549995962752000}{3597816638935238023393139004929617550671814203943803914277128680638811}\cdot t^9+\frac{126284228464349020717159178687555457694023969395974708484858682603525810059270466027564935040000}{3597816638935238023393139004929617550671814203943803914277128680638811}\cdot t^8-\frac{365696728374240721832568040826519437060849251097035247738027947644167761316471854827078355456000}{3597816638935238023393139004929617550671814203943803914277128680638811}\cdot t^7+\frac{762743064589964349406485264710207781144941758679295174337805434162313633541407534124030660096000}{3597816638935238023393139004929617550671814203943803914277128680638811}\cdot t^6-\frac{1106259238114574308218377546498815651868449713900595389888399365011885947471026533448384050176000}{3597816638935238023393139004929617550671814203943803914277128680638811}\cdot t^5+\frac{1064285997897207986621413988830367442662468415089185553928667162825522828424667711166317941760000}{3597816638935238023393139004929617550671814203943803914277128680638811}\cdot t^4-\frac{634740137324018265511673521836487993166598879932009891848830106088738466802367228699042918400000}{3597816638935238023393139004929617550671814203943803914277128680638811}\cdot t^3+\frac{210433456143898885502201420602284623541782731837818581716356847983922495503699035619308359680000}{3597816638935238023393139004929617550671814203943803914277128680638811}\cdot t^2-\frac{31397075787139551703547338904761707873892774535705138434600181460846231866818733889671700480000}{3597816638935238023393139004929617550671814203943803914277128680638811}\cdot t+\frac{1211572023660840046702216222537753000832413289963053308408879605124278259011585144191918080000}{3597816638935238023393139004929617550671814203943803914277128680638811}$

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.