Rule: Q[1, 14, 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.

• $P_1$:
  $t$
• $P_2$:
  $t^{15}-\frac{105}{29}\cdot t^{13}+\frac{455}{87}\cdot t^{11}-\frac{1001}{261}\cdot t^9+\frac{1001}{667}\cdot t^7-\frac{1001}{3335}\cdot t^5+\frac{1001}{38019}\cdot t^3-\frac{143}{215441}\cdot t$
• $P_3$:
  $t^{47}-\frac{8091075286098004762496554612311620012216797329478847923844531}{682017498410650123495569673233542411330397195511301746733439}\cdot t^{45}+\frac{1153496330017058993925330973697075325069617409991465233321470185}{17505115792540019836386288279660921890813528018123411499491601}\cdot t^{43}-\frac{2987450209967901130577051813991491342173767612204007861251632213221}{13121334651922497725931264943340122451585511644441934305404632921}\cdot t^{41}+\frac{36243541162346809831540693806951259798955699478344834205041348489810939}{66092162641733621045515781519604196788636222153054023096323136023077}\cdot t^{39}-\frac{263713132323409515702322909208332038711508231552098819814551997895039323}{269686410779487764036300028039764251263975389245220439071203601013705}\cdot t^{37}+\frac{596572655368667432820015909120265309118313488665058742552500026137371177411}{445791637018493273952003946349730307339351318422349385784699552475654365}\cdot t^{35}-\frac{3066534146167367443021755086674061958121823870589095496594651590182345818918541}{2132578033169068123931596478547839844249988837068834991716845719133035351287}\cdot t^{33}+\frac{1829503965249056645668889673659180736679808138918769750701261366638692939282250}{1486342265542077783346264212321221709628780098563127418469316713335145850897}\cdot t^{31}-\frac{303808444742105917157055964029196786847678668414688828806657070321225547005542}{358772270992915327014615499525812136806946920342823859630524723908483481251}\cdot t^{29}+\frac{1084759752139317325951401478523825284531726662579493755376122082722289313362618}{2306393170668741387951099639808792308044658773632439097624801796554536665185}\cdot t^{27}-\frac{18031869519824621118113568886046536749620463690500863801555393617945146031206}{85421969284027458813003690363288604001654028653053299912029696168686543155}\cdot t^{25}+\frac{1077956160185580716431507808986740404264105808005138513622824175376869304730}{14113194925187145369104957538282465008968926473113153898509254149609081043}\cdot t^{23}-\frac{938074137447933241158867539322041861514818859742801132559830834617512770070}{42339584775561436107314872614847395026906779419339461695527762448827243129}\cdot t^{21}+\frac{130458381837320677261508328655501579144811665538070516032847672482466843568550}{25550082412719065224268590760226418363868640205035429191948569209689661086109}\cdot t^{19}-\frac{24446968623026101219327715856124716763670676669226624156672232746809191982900710}{26495435461989670637566528618354795843331779892621740072050666270448178546295033}\cdot t^{17}+\frac{29416516104071199977007246283794236467736472039330382347362104239463326932061815}{229107588994851857866016453346950293468810096718552693564202820103287190959139403}\cdot t^{15}-\frac{146442712305907678761268758877413558710510522094442228291014678599421491772575}{10909885190231040850762688254616680641371909367550128264962039052537485283768543}\cdot t^{13}+\frac{3705953280634300630983944014524858584710623973800776336063165158664040909505}{3636628396743680283587562751538893547123969789183376088320679684179161761256181}\cdot t^{11}-\frac{478103959306678248735256698561341161283417326096577743068562467619469156645}{8926269701098124332442199481050011433849744027995559489514395588439760686719717}\cdot t^9+\frac{1801690286586865613046281760957328881422708676416534687121565797570353191}{991807744566458259160244386783334603761082669777284387723821732048862298524413}\cdot t^7-\frac{35278688319719015065468369370799816975020773777851325302191489983366699}{991807744566458259160244386783334603761082669777284387723821732048862298524413}\cdot t^5+\frac{18498667294081754579301708930228920969275264068077281266475096360865}{56140061013195750518504399251886864363834868100601003078706890493331828218363}\cdot t^3-\frac{6339999823056970026701232630842665334613977200832663974707777026165}{6942654211965207814121710707483342226327578688440990714066752124342036089670891}\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.