Rule: Q[4, 5, 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.

• $P_1$:
  $\frac{35}{8}\cdot t^4-\frac{15}{4}\cdot t^2+\frac{3}{8}$
• $P_2$:
  $\frac{35}{8}\cdot t^9-\frac{855}{88}\cdot t^7+\frac{45297}{6292}\cdot t^5-\frac{24885}{12584}\cdot t^3+\frac{1845}{12584}\cdot t$
• $P_3$:
  $\frac{35}{8}\cdot t^{27}-\frac{17051623981426098121518663647625088809428655}{585364767164693998181033410799179225938796}\cdot t^{25}+\frac{18000580010832558446771895042777371086445214015123}{208765661291150796899280117694240877497264083032}\cdot t^{23}-\frac{116338009644942225880896574532192736503634158407863}{778126555721562061170044075042170543398893400392}\cdot t^{21}+\frac{4260077402805391864298131540313779976368603680525867}{25289113060950766988026432438870542660464035512740}\cdot t^{19}-\frac{241970246961921950827601193275519168424691008233489139}{1871394366510356757113956000476420156874338627942760}\cdot t^{17}+\frac{322485432350109610159424452277009071858924440883644993}{4678485916275891892784890001191050392185846569856900}\cdot t^{15}-\frac{262888332727470865420265803176201283930249543718690277}{10292669015806962164126758002620310862808862453685180}\cdot t^{13}+\frac{317989204387031156516166321001075956931796153881184091}{49088113767694742628912230474035328730319190163729320}\cdot t^{11}-\frac{475510678394976006847180747876504253953884129137331}{437209858496052683119918514664319574072253229345255}\cdot t^9+\frac{14755161481203080628380211544631944400092238650904703}{129414118114831594203495880340638593925386955886195480}\cdot t^7-\frac{21835786202536199470279622914542139535067810868212009}{3235352952870789855087397008515964848134673897154887000}\cdot t^5+\frac{15116401092486036731341121958471485158851832972629}{80883823821769746377184925212899121203366847428872175}\cdot t^3-\frac{269285006023900657557916585857041156167659921939}{173604304788188723931518863871588357704787379847335400}\cdot t$

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.