Rule: Q[2, 7, 26]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^9-\frac{151}{50}\cdot t^7+\frac{1281}{650}\cdot t^5-\frac{651}{1430}\cdot t^3+\frac{56}{2145}\cdot t$
• $P_3$:
  $\frac{3}{2}\cdot t^{35}-\frac{312853898935481831785901007190647975576110829747241014143}{24275882682476806243254855773553737039558365105738267150}\cdot t^{33}+\frac{943868995230736288783653597588505947913015489054252362285813}{18619602017459710388576474378315716309341266036101250904050}\cdot t^{31}-\frac{1203266758496823265838538249425658559517779704600014467538488905}{9948080965888374066408638730846520909754851617768176333015834}\cdot t^{29}+\frac{40121607428700632287486987585911028570271722094759163772480136488001}{205179169921447715119678173823709493763693814616468636868451576250}\cdot t^{27}-\frac{63181700618368390730312959153337701591688220167713043122560849068259}{278833230918890484649819056734784696653224927555713788564818808750}\cdot t^{25}+\frac{2165622758106695812026726297915148698012259772197940656513026595959}{11153329236755619385992762269391387866128997102228551542592752350}\cdot t^{23}-\frac{888100666623448989170654684583512466048150968843167279861974904707}{7097573150662666881995394171430883187536634519599987345286296950}\cdot t^{21}+\frac{30635703548453228621552889725281809793141058480066151056444709987}{501632989595707283389148159484588736562739582588269782298430010}\cdot t^{19}-\frac{7646404723018122154254190808256561960782479742542475885518250619}{338941209186288704992667675327424822001851069316398501552993250}\cdot t^{17}+\frac{78462239490981956688565441158449264622436906914560397603634552851}{12540824739892682084728703987114718414068489564706744557460750250}\cdot t^{15}-\frac{3215390992540735555067070153961838470432141205403553787333315463}{2508164947978536416945740797422943682813697912941348911492150050}\cdot t^{13}+\frac{8947508570668281630415293559081605842525671807096452346840539}{47323866942991253149919637687225352505918828546063187009285850}\cdot t^{11}-\frac{630762889392341850125209328494042931774006392264767830643753478229}{32722021544317581802757523591339207874724065711815426169108887982310}\cdot t^9+\frac{7304151351568216372757674539044360217594477773795097490154887001847}{5726353770255576815482566628484361378076711499567699579594055396904250}\cdot t^7-\frac{5775106543962584532833747594057056606136369305160933309322398330751}{116981227020935354944858146839037668152138534919740148554564274536758250}\cdot t^5+\frac{10790922049005044898728184112420097746544896101811422527096937153}{11698122702093535494485814683903766815213853491974014855456427453675825}\cdot t^3-\frac{61996388165118553729415070979058964971198067811201745493426672}{11698122702093535494485814683903766815213853491974014855456427453675825}\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.