Rule: Q[2, 3, 42]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^5-\frac{25}{14}\cdot t^3+\frac{3}{7}\cdot t$
• $P_3$:
  $\frac{3}{2}\cdot t^{47}-\frac{419757505899975397972370036053758346919375}{23742308300227482407777430419893170688408}\cdot t^{45}+\frac{67213429085150289851175207321186931769569815}{688526940706596989825545482176901949963832}\cdot t^{43}-\frac{70125799592829610682497632222478387760970033}{209017107000216943339897735660845234810449}\cdot t^{41}+\frac{55816233622067572464097630325347009990914700725}{69393679524072025188846048239400617957069068}\cdot t^{39}-\frac{198287470915277901295384240854896410068170405787}{138787359048144050377692096478801235914138136}\cdot t^{37}+\frac{21372290588851834980885568884350265236791672154805}{10964201364803379979837675621825297637216912744}\cdot t^{35}-\frac{2021927696912791041140682764639298161708400671065}{967429532188533527632736084278702732695609948}\cdot t^{33}+\frac{5042102642488576542065993308183272296952659811686}{2821669468883222788928813579146216303695529015}\cdot t^{31}-\frac{607666626247824471974878242381433632007750326013285}{494356490948340632620328139066417096407456683428}\cdot t^{29}+\frac{1772549652225501712909379553177972689469765545010851}{2593545137241294451924381616284404963911041220940}\cdot t^{27}-\frac{56076573635047430179206964160923362116568596991}{182387140452974293384274375266132557237063377}\cdot t^{25}+\frac{215590025904072794694298660474283508660205527101205}{1930750268835185869765928536567279250911552908922}\cdot t^{23}-\frac{125728572241339902470428591421559786242094421476449}{3861500537670371739531857073134558501823105817844}\cdot t^{21}+\frac{29173434498107480731409431367182083922204289408025}{3861500537670371739531857073134558501823105817844}\cdot t^{19}-\frac{1135235155007855648107575334640059083303674819145219}{824430364792624366390051485114228240139233092109694}\cdot t^{17}+\frac{9418567731089059881057753846073048076646078164231305}{48641391522764837617013037621739466168214752434471946}\cdot t^{15}-\frac{569744709015480662940408616289624852502174077846595}{27795080870151335781150307212422552096122715676841112}\cdot t^{13}+\frac{555651184839555373340653665000031432707860176601}{351836466710776402293041863448386735393958426289128}\cdot t^{11}-\frac{46646089212417675909926493963509456102723138068250}{552427232294257798650362355846898222910438974077217101}\cdot t^9+\frac{36571359552173136624555429943680030996469167184977}{12521683932003176769408213399196359719303283412416920956}\cdot t^7-\frac{10252588659037341282053435103477767534575386072645}{175303575048044474771714987588749036070245967773836893384}\cdot t^5+\frac{681914383622955789474583634937795570712041830995}{1227125025336311323402004913121243252491721774416858253688}\cdot t^3-\frac{972278741126383990987645646175414596497779873}{613562512668155661701002456560621626245860887208429126844}\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.