Rule: Q[3, 14, 18]

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.

• $P_1$:
  $\frac{5}{2}\cdot t^3-\frac{3}{2}\cdot t$
• $P_2$:
  $\frac{5}{2}\cdot t^{17}-\frac{2660449}{261516}\cdot t^{15}+\frac{1384565}{81548}\cdot t^{13}-\frac{340471495}{22751892}\cdot t^{11}+\frac{17578561}{2353644}\cdot t^9-\frac{366222857}{174431172}\cdot t^7+\frac{90173083}{290718620}\cdot t^5-\frac{202159529}{9942576804}\cdot t^3+\frac{1267981}{3314192268}\cdot t$
• $P_3$:
  $\frac{5}{2}\cdot t^{35}-\frac{45493194219318860710962096802101601694183499955596747291761953784623}{2106417718097572147346761900735350815366527917701412909125307956580}\cdot t^{33}+\frac{8676599689047613091834778249645188753332837520666119990071893838715507}{101810189708049320455093491868875289409382182688901623941056551234700}\cdot t^{31}-\frac{15633488572873226115287510208430596557709132454074235488506889349348837}{76850272231237228988683474507473605554178808868396709684539461254580}\cdot t^{29}+\frac{4251164380954212385793232833709899609256736301139641604617653128363186848441}{12964707175644402631450375152406062320443029003347549403703948958010796500}\cdot t^{27}-\frac{181175408917938605927512916688817295737843974212264641751391353356539939463}{480174339838681578942606487126150456312704777901761089026072183630029500}\cdot t^{25}+\frac{229351435598921337608049688875346161249539599330203567598924747632177053162469}{717860638058828960519196698253594932187493642963132828093977914526894102500}\cdot t^{23}-\frac{4380062252248397918564725820820341669498756493424016370922982958148301277264248071}{21656326094962483538035232184649462314893327243480100314526765641371533428467500}\cdot t^{21}+\frac{67324767670533742634175845668384814570298030115392692836321659643305273936404807801}{699269283982030375046815280980531173281262562825190784881148128676520392571212500}\cdot t^{19}-\frac{213875664565132865540439930592005149192844369506161458414284789347709330926735558933}{6219816262787533335942725393984724646554388058813539086574422828754312965501837500}\cdot t^{17}+\frac{220452015936477321255861330509681653721047781435989239344810803534793411953130305119209}{24163986180929567010137488155630655251863797608490599351341632689710505870974638687500}\cdot t^{15}-\frac{31252311563683361512302732936311099639289369219112431880048784057219270390543596237}{17702553978702979494606218429033447070962489090469303554096434204916121517197537500}\cdot t^{13}+\frac{398522143663527737959253581154275021587029690063042192136517840081933108118922946277}{1646337520019377092998378313900110577599511485413645230530968381057199301099370987500}\cdot t^{11}-\frac{3224431441305436310339524565757653285154812175772656076436727075493823394929611901351}{143231364241685807090858913309309620251157499230987135056194249151976339195645275912500}\cdot t^9+\frac{3440403579280576452391342679005460062969809957068589107457300808306907088171138583}{2590748190418089533943184478462964707385277763867984355021601405849701225761025662500}\cdot t^7-\frac{17735150630130393813259847707160947979512954948733219877687919535964797764634385051}{397864900671349464141274759192526722919881942308297597378317358755489831099014655312500}\cdot t^5+\frac{166910549683047673135620295270599670913222045931746375398947160924047044413965839}{238718940402809678484764855515516033751929165384978558426990415253293898659408793187500}\cdot t^3-\frac{20785772712040510536590963891265135415594240262513719555219911090575868286720993}{6405624900808726372674523622999680239010099271163591317790909475963386280694135950531250}\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.