Rule: Q[19, 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.

• $P_1$:
  $\frac{4418157975}{65536}\cdot t^{19}-\frac{20419054425}{65536}\cdot t^{17}+\frac{9917826435}{16384}\cdot t^{15}-\frac{10518906825}{16384}\cdot t^{13}+\frac{13233463425}{32768}\cdot t^{11}-\frac{5019589575}{32768}\cdot t^9+\frac{557732175}{16384}\cdot t^7-\frac{66927861}{16384}\cdot t^5+\frac{14549535}{65536}\cdot t^3-\frac{230945}{65536}\cdot t$
• $P_2$:
  $\frac{4418157975}{65536}\cdot t^{39}-\frac{1764994406175}{2686976}\cdot t^{37}+\frac{13993357449723795}{4737138688}\cdot t^{35}-\frac{1579366441254622475}{194222686208}\cdot t^{33}+\frac{61654248760023938443425}{4023371500470272}\cdot t^{31}-\frac{3454896613681299215854425}{164958231519281152}\cdot t^{29}+\frac{318275093135270417664911468075}{14831889470593126219776}\cdot t^{27}-\frac{180503068878177443308656837423189}{10743231939866287758524416}\cdot t^{25}+\frac{18080847685692792560832821174239195725}{1780389883538520939918183268352}\cdot t^{23}-\frac{415468490778581502373498848380521896033025}{87376194314419992168364680260911104}\cdot t^{21}+\frac{744610289726493651991825773502318854257801675}{432790933523953539303656616509485252608}\cdot t^{19}-\frac{3623967155455233980726035493254368954487075}{7592823395157079636906256429990969344}\cdot t^{17}+\frac{67066436161363862522956802807759126612605}{669955005455036438550552037940379648}\cdot t^{15}-\frac{3470095034143321217709646493973626414575}{223318335151678812850184012646793216}\cdot t^{13}+\frac{386413950750358912848634478053016396525}{223318335151678812850184012646793216}\cdot t^{11}-\frac{88495118383487208705057029847234389575}{669955005455036438550552037940379648}\cdot t^9+\frac{40373524755254969001458195194073350725}{6252913384247006759805152354110210048}\cdot t^7-\frac{485463882874910071579655477444669065}{2679820021820145754202208151761518592}\cdot t^5+\frac{57757866445719049699451821134021775}{24118380196381311787819873365853667328}\cdot t^3-\frac{75960419859873401339723448222725}{8039460065460437262606624455284555776}\cdot t$

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.