Rule: Q[18, 20]

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.

• $P_1$:
  $\frac{2268783825}{65536}\cdot t^{18}-\frac{9917826435}{65536}\cdot t^{16}+\frac{4508102925}{16384}\cdot t^{14}-\frac{4411154475}{16384}\cdot t^{12}+\frac{5019589575}{32768}\cdot t^{10}-\frac{1673196525}{32768}\cdot t^8+\frac{156165009}{16384}\cdot t^6-\frac{14549535}{16384}\cdot t^4+\frac{2078505}{65536}\cdot t^2-\frac{12155}{65536}$
• $P_2$:
  $\frac{2268783825}{65536}\cdot t^{38}-\frac{272621385905}{851968}\cdot t^{36}+\frac{1851310344692725}{1362296832}\cdot t^{34}-\frac{8029678148247511525}{2284571787264}\cdot t^{32}+\frac{5649602524679265100025}{913257571958784}\cdot t^{30}-\frac{13129216950455215903094725}{1674001129400451072}\cdot t^{28}+\frac{851142879683671291770421770479}{115099295654186814357504}\cdot t^{26}-\frac{402782543171944966331236859272525}{76310833018725857919025152}\cdot t^{24}+\frac{260380430575859786671071697168928218025}{90539598321731443934890743791616}\cdot t^{22}-\frac{25972575433171780709165945538431107441775}{21690700912220518782687396762648576}\cdot t^{20}+\frac{617656014504874466181829592245536301593933725}{1630121245656108648075305928903328432128}\cdot t^{18}-\frac{959138205296233439106982655034869922113065}{10654387226510514039707881888257048576}\cdot t^{16}+\frac{11076296042599795051109807605058733496475}{703591609297864134697690313375465472}\cdot t^{14}-\frac{2417372297517211459610495178927960743675}{1229352372289674696889370987106582528}\cdot t^{12}+\frac{68767416862321403293857521960142361975}{409784124096558232296456995702194176}\cdot t^{10}-\frac{8745885630637310210411089014606537575}{956162956225302542025066323305119744}\cdot t^8+\frac{4213846106672615016617542700997154505}{14752228467476096362672451845278990336}\cdot t^6-\frac{20646121895650116197476164995001775}{4917409489158698787557483948426330112}\cdot t^4+\frac{272040590670456351810196449973775}{14752228467476096362672451845278990336}\cdot t^2-\frac{81199635657983392050807454775}{309796797816998023616121488750858797056}$

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.