Rule: Q[2, 6, 39]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^8-\frac{161}{52}\cdot t^6+\frac{105}{52}\cdot t^4-\frac{245}{572}\cdot t^2+\frac{25}{1716}$
• $P_3$:
  $\frac{3}{2}\cdot t^{47}-\frac{12085604879212642500508495564069472085330342395182695066755756587983377}{679952931579439683395895285116044556949008937608580102032880981764164}\cdot t^{45}+\frac{2292919297197187551753815495271272800829472905395453689117020581839832455}{23238391367509085650177362391318934563963187808857943487123755906175252}\cdot t^{43}-\frac{12450609003328803294384061987582206619186969194524909233963843231397073155}{36517472148942848878850140900644040029085009413919625479765902138275396}\cdot t^{41}+\frac{120915980341384939403715013343823430231792105945375188004069224469776152771555}{147128895288090738132887217688694837277183502928682171057976819715111570484}\cdot t^{39}-\frac{19379350879127042472583659883455410895918690580185112345578055486909326539807}{13203875218161989319618083638729023858208775903856092274433817153920269146}\cdot t^{37}+\frac{104432620236673671019885688446778623967830350802462758241128511995419670359763}{51872366928493529469928185723578308014391619622291791078132853104686771645}\cdot t^{35}-\frac{580059368716517726119519061640041596113781657806963278334904982787893087373013}{267295255466825481268571121728556457768276816406632994026143407762974188006}\cdot t^{33}+\frac{536312817005772553307666565223119924661419419925254685529195882253245177529312}{287544896032494078334371964283750128811328090376832463270548211381381323461}\cdot t^{31}-\frac{15574318734327737068712911591985278526514986285119294644900406387332189722720971}{12076885633364751290043622499917505410075779795826963457363024878018015585362}\cdot t^{29}+\frac{1249436224826230817958938419510046055109971283319232476530362339703912063567191407}{1733895723075939292356262944631013276732308384972299753521405714629729380469830}\cdot t^{27}-\frac{62752629498408226000859033078975872487158217080957269459284482250798324988847107}{192655080341771032484029216070112586303589820552477750391267301625525486718870}\cdot t^{25}+\frac{32052114482397541114595567428250454742320659631720691685971888414460685719979285}{269717112478479445477640902498157620825025748773468850547774222275735681406418}\cdot t^{23}-\frac{3717997295427016499722921833641530353431652140256089927026443357561877134681940}{106835999098618481650234383457062434222899809579101297944248230901427769907737}\cdot t^{21}+\frac{7307813158668064002287330911460611905035349702373377600778954250402854917059108595}{901375324395044129683027493227235757538605693418877650755622324115346094711577069}\cdot t^{19}-\frac{1336827730328303889025387603779723803193412385585524700506953922665743453930885394}{901375324395044129683027493227235757538605693418877650755622324115346094711577069}\cdot t^{17}+\frac{2640410309976858949453613830740993988261347382389586624653272947822834079828737091}{12619254541530617815562384905181300605540479707864287110578712537614845325962078966}\cdot t^{15}-\frac{880982363073818794015246631525304990732575287646194929527273095314275014058322015}{39660514273381941706053209701998373331698650510430616633247382261075228167309391036}\cdot t^{13}+\frac{88973708416830548750031193606606544953972832040918600569219878986629012553966305}{51863749434422539154069581917997872818375158359793883289631192187559913757250742124}\cdot t^{11}-\frac{198574230915642704393724684284922589254943609619091649054664995928923527102742285}{2160804662265165789033989907610275011379469833054300239088324162210049668891660598332}\cdot t^9+\frac{327534788698329853704145503133276261308726650858171584031261886163926217489389}{102895460107865037573047138457632143399022373002585725670872579152859508042460028492}\cdot t^7-\frac{55801070115871136264686444485862440492376793945993838919317577672343555715555}{874611410916852819370900676889873218891690170521978668202416922799305818360910242182}\cdot t^5+\frac{3357251079560204720965848672644368307364402630912637890170307674028802860}{5535515258967422907410763777784007714504368167860624482293777992400669736461457229}\cdot t^3-\frac{10589024204798489147270259926272101673462801819017286785456903859000647525}{6122279876417969735596304738229112532241831193653850677416918459595140728526371695274}\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.