Rule: Q[4, 41]

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.

• $P_1$:
  $\frac{35}{8}\cdot t^4-\frac{15}{4}\cdot t^2+\frac{3}{8}$
• $P_2$:
  $\frac{35}{8}\cdot t^{45}-\frac{355007147150647258821752481855}{7277148538047608236822550828}\cdot t^{43}+\frac{260927342118465613508357162049962943}{1028013665375833425182974465268248}\cdot t^{41}-\frac{630984609656923052131908590356784095}{771010249031875068887230848951186}\cdot t^{39}+\frac{7829569018378049165568113982529010695}{4274372608667938978392367513483768}\cdot t^{37}-\frac{174509742079468076637265309575936475}{57761792009026202410707669101132}\cdot t^{35}+\frac{77558288406591876539558375883232823}{20386514826715130262602706741576}\cdot t^{33}-\frac{1159316816570127779228163306543918182}{310044912989625939410416165028135}\cdot t^{31}+\frac{51213670017895389978561497838526971659}{17610551057810753358511638173598068}\cdot t^{29}-\frac{3287873493882978329122200424646106501023}{1822692034483412972605954550967400038}\cdot t^{27}+\frac{24297279484561807456668257842710705964449}{27137859180086370925466434425514622788}\cdot t^{25}-\frac{2411137104783452758660493931879835113045}{6784464795021592731366608606378655697}\cdot t^{23}+\frac{132552478604447847953837095457086673063}{1179906920873320475020279757631070556}\cdot t^{21}-\frac{12779970460377956110337353068783744585}{455533684640965499849601678579084202}\cdot t^{19}+\frac{23218013532864959972023360589672952384015}{4246485008223080389597986847714222931044}\cdot t^{17}-\frac{867581078941069254435191072568747102490}{1061621252055770097399496711928555732761}\cdot t^{15}+\frac{776662475629294187013362764841491676775}{8492970016446160779195973695428445862088}\cdot t^{13}-\frac{1667530861111337283417611887067378819877}{225063705435823260648693302928853815345332}\cdot t^{11}+\frac{9516165319442041078506311585317047987295}{22956497954453972586166716898743089165223864}\cdot t^9-\frac{199975943746341118412451541356557140365}{13391290473431484008597251524266802013047254}\cdot t^7+\frac{31620016375504801794457456711703384415}{101990809320036803579337702440684470768880152}\cdot t^5-\frac{10388677008659762901112701017518948485}{3416692112221232919907813031762929770757485092}\cdot t^3+\frac{426234984999273938019004051995681213}{47833689571097260878709382444681016790604791288}\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.