Rule: Q[9, 28]

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.

• $P_1$:
  $\frac{12155}{128}\cdot t^9-\frac{6435}{32}\cdot t^7+\frac{9009}{64}\cdot t^5-\frac{1155}{32}\cdot t^3+\frac{315}{128}\cdot t$
• $P_2$:
  $\frac{12155}{128}\cdot t^{37}-\frac{6253798538414906122679116457000032045}{7339327205962890753476248481066688}\cdot t^{35}+\frac{95067731403851125305967193538452065998389}{27082117390003066880327356895136078720}\cdot t^{33}-\frac{100955828480734222925629869982622333613551}{11472285838820743609027560906967366680}\cdot t^{31}+\frac{23757850949788493594400823140453141725608393447}{1583863782907591862662345058815914643840800}\cdot t^{29}-\frac{830608648602881486884525220889101676228718750241}{45140117812866368085876834176253567349462800}\cdot t^{27}+\frac{237248539527906362977337103020477191272614477891}{14146475667849858944291885354381459853108000}\cdot t^{25}-\frac{3768385482118395981828140567455727964896773657}{325984004520018488716291271209659727049880}\cdot t^{23}+\frac{4321972653228745051109331698123542704049884431}{711237828043676702653726409911984859017920}\cdot t^{21}-\frac{289085496761826110108647760738289180018952253}{118539638007279450442287734985330809836320}\cdot t^{19}+\frac{3091514850843378284353763042864839513729149}{4159285544115068436571499473169502099520}\cdot t^{17}-\frac{1326040663931248163670622867339036880841773}{7798660395215753318571561512192816436600}\cdot t^{15}+\frac{7683945869250866850062095059231348843725419}{268273917595421914158861716019432885419040}\cdot t^{13}-\frac{56964295735121706289653492285693548486386987}{16498845932118447720769995535195122453270960}\cdot t^{11}+\frac{9301108778065979705360372477875651905189660151}{32568721870001815800799971186475171722756875040}\cdot t^9-\frac{13765198765279954070795615548934706696301493}{904686718611161550022221421846532547854357640}\cdot t^7+\frac{4875544885400025087956772419636187808176521}{10339276784127560571682530535388943404049801600}\cdot t^5-\frac{3129117385139638916222090958505563704405261}{443554974039072348525180559968185672033736488640}\cdot t^3+\frac{9683742760613877026474740465158122784323}{295703316026048232350120373312123781355824325760}\cdot t$

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.