Rule: Q[6, 8, 14]

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.

• $P_1$:
  $\frac{231}{16}\cdot t^6-\frac{315}{16}\cdot t^4+\frac{105}{16}\cdot t^2-\frac{5}{16}$
• $P_2$:
  $\frac{231}{16}\cdot t^{14}-\frac{3731}{80}\cdot t^{12}+\frac{1182181}{20400}\cdot t^{10}-\frac{200960617}{5814000}\cdot t^8+\frac{14859361517}{1482570000}\cdot t^6-\frac{123220867}{98838000}\cdot t^4+\frac{4422019}{98838000}\cdot t^2-\frac{22771}{889542000}$
• $P_3$:
  $\frac{231}{16}\cdot t^{28}-\frac{66692493727151796794988446333257645296440476866860128033}{663597268983353931807422985370501093993478178076901520}\cdot t^{26}+\frac{816847678131405704218368149283385868396031002842444010203039}{2622868205656706415468839349676905574009222498848953257800}\cdot t^{24}-\frac{52902511698294444121244888611741925564991533881986676818448256}{93439679826520166051077401832239761074078551521493959809125}\cdot t^{22}+\frac{7405854545331890169733841168915974072331836896857761098165302200709}{11055782917073866047163478184790608530284974216023165324615670000}\cdot t^{20}-\frac{4720850890743672091813865876576510941755530915498890165728681135959}{8728249671374104774076430145887322523909190170544604203643950000}\cdot t^{18}+\frac{268734920441836360320773975048366904677094383108487189898188337031}{884234443832017150314932465759826791637859134924453367035825000}\cdot t^{16}-\frac{2821882549790272258728578066926496162659998811357899308972650177126}{23719588955793860057198063394007353685685571294348461570736005625}\cdot t^{14}+\frac{65496969198730063814468456227107829860149419790124725879878070747987}{2049372485780589508941912677242235358443233359831707079711590886000}\cdot t^{12}-\frac{97367264164004178962048425403998904508921817226742092674526672010679}{17078104048171579241182605643685294653693611331930892330929924050000}\cdot t^{10}+\frac{3024693700013173972320540179681507292631323504966042350929983260741}{4743917791158772011439612678801470737137114258869692314147201125000}\cdot t^8-\frac{72059093464365348661379919420964637532658646403937856563781448194}{1778969171684539504289854754550551526426417847076134617805200421875}\cdot t^6+\frac{131903547531475184411735058229049663392298788239108160198163257037}{108161325638420001860823169076673532806726205102228984762556185650000}\cdot t^4-\frac{12805183013790677239764371321010257567344108179919607456444457877}{1103245521511884018980396324582070034628607292042735644578073093630000}\cdot t^2+\frac{52503378606980613389131885508938840451296119842593790874174029}{8274341411339130142352972434365525259714554690320517334335548202225000}$

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.