Rule: Q[4, 5, 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.

• $P_1$:
  $\frac{35}{8}\cdot t^4-\frac{15}{4}\cdot t^2+\frac{3}{8}$
• $P_2$:
  $\frac{35}{8}\cdot t^9-\frac{855}{88}\cdot t^7+\frac{45297}{6292}\cdot t^5-\frac{24885}{12584}\cdot t^3+\frac{1845}{12584}\cdot t$
• $P_3$:
  $\frac{35}{8}\cdot t^{37}-\frac{257472905352985429977813406576309874567525501107174200799866831750572295}{6267578758349973388506161314660174986081400567263366359640710231584424}\cdot t^{35}+\frac{770460909225556733074106451068241637234350157643017567766308939381620013727}{4343432079536531558234769791059501265354410593113512887231012190488005832}\cdot t^{33}-\frac{24366285190463984139145570830384151139817239325772523944398358201636835365831}{52186994531401053419396552186517947021606781823318419993548373743287706436}\cdot t^{31}+\frac{103939000036556908629580738322999968987779123445655489368237286514567728506709}{124154543441639602892919216895345115898177424499023660468522340760240914505}\cdot t^{29}-\frac{4377158803736069087652511411392843016910655280185743095510472981507976742163413}{4043890843527689922797940207448383774969207540825342083831870527619275501020}\cdot t^{27}+\frac{52124287332127084732723044716884117448537510769107652351753686298786299548689}{50025640214580059773703713767355174904027533680925284437866144628668500350}\cdot t^{25}-\frac{3063666237206675950365479848603969415882543135175734294441594382750693323263743}{4030065575686569615369571181098132890268458113335340914314496611285534388196}\cdot t^{23}+\frac{155314509641117412986162985387368975654207073927078837099314191159081985427501}{366369597789688146851779198281648444569859828485030992210408782844139489836}\cdot t^{21}-\frac{1623719124273245714782174488377517036470554891457608872547536553551297897050631}{8976055145847359597868590357900386891961565797883259309155015179681417500982}\cdot t^{19}+\frac{2608843690306771550066466008691344741610757112891920179023679119204195696474043}{44407851774192200115770920718033493044441430789527703950556390888950170794332}\cdot t^{17}-\frac{9556360397757187387146564117869572961041354029260173943510751553212724541550613}{666117776612883001736563810770502395666621461842915559258345863334252561914980}\cdot t^{15}+\frac{315086836103375312993516650708812746060927414425732283513048568338959278916}{121999592786242308010359672302289816056157776894306878985045029914698271413}\cdot t^{13}-\frac{73211737246770275085588527956358738120471610974220025349660657005594576399283}{220087265386381123650688848833330828165308629517329609689021233966115681629052}\cdot t^{11}+\frac{491934985380476960753874557851583958093835393036474607217474923358767224827991}{16776652002407324743736599976977081765146480531843716156749482243689818095087282}\cdot t^9-\frac{451109435080261503366128683528932472188949332520096739773633815176454069207}{272791089470037800711164227267920028701568789135670181410560686889265334879468}\cdot t^7+\frac{544751551570473939835725922726063769474679467955659464252890255445332605650371}{10177835548127110344533537319366096270855531522651854468428019227838489644352951080}\cdot t^5-\frac{18284298204940617492176352506441883773738418494399129845098561198143790237483}{22391238205879642757973782102605411795882169349834079830541642301244677217576492376}\cdot t^3+\frac{63000647237790689854367113883229719391018688436175634794327670384281717771}{16929960594689485987736274272701652821276762191337962798702217349721585213289543016}\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.