Rule: Q[18, 19]

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.

• $P_1$:
  $\frac{2268783825}{65536}\cdot t^{18}-\frac{9917826435}{65536}\cdot t^{16}+\frac{4508102925}{16384}\cdot t^{14}-\frac{4411154475}{16384}\cdot t^{12}+\frac{5019589575}{32768}\cdot t^{10}-\frac{1673196525}{32768}\cdot t^8+\frac{156165009}{16384}\cdot t^6-\frac{14549535}{16384}\cdot t^4+\frac{2078505}{65536}\cdot t^2-\frac{12155}{65536}$
• $P_2$:
  $\frac{2268783825}{65536}\cdot t^{37}-\frac{272621385905}{851968}\cdot t^{35}+\frac{1851310344692725}{1362296832}\cdot t^{33}-\frac{8029678148247511525}{2284571787264}\cdot t^{31}+\frac{5649602524679265100025}{913257571958784}\cdot t^{29}-\frac{13129216950455215903094725}{1674001129400451072}\cdot t^{27}+\frac{851142879683671291770421770479}{115099295654186814357504}\cdot t^{25}-\frac{402782543171944966331236859272525}{76310833018725857919025152}\cdot t^{23}+\frac{260380430575859786671071697168928218025}{90539598321731443934890743791616}\cdot t^{21}-\frac{25972575433171780709165945538431107441775}{21690700912220518782687396762648576}\cdot t^{19}+\frac{107433300454893130871075079842332165925}{283538574015954493891338519773184}\cdot t^{17}-\frac{178674634974610936143539550240599973445}{1984770018111681457239369638412288}\cdot t^{15}+\frac{16094740239736158509580942084609425}{1022374665922912838550499470336}\cdot t^{13}-\frac{5361000957536406052379975086942475}{2726332442461100902801331920896}\cdot t^{11}+\frac{610020696904709476641000860049925}{3635109923281467870401775894528}\cdot t^9-\frac{6284168272845163663383425219068975}{687035775500197427505935644065792}\cdot t^7+\frac{18689195795795389847646427798375}{65431978619066421667231966101504}\cdot t^5-\frac{823917237768556523080128682625}{196295935857199265001695898304512}\cdot t^3+\frac{37915766944646708900332903375}{2061107326500592282517806932197376}\cdot t$

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.