Rule: Q[8, 16]

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.

• $P_1$:
  $\frac{1}{40320}\cdot t^8-\frac{1}{630}\cdot t^7+\frac{7}{180}\cdot t^6-\frac{7}{15}\cdot t^5+\frac{35}{12}\cdot t^4-\frac{28}{3}\cdot t^3+14\cdot t^2-8\cdot t+1$
• $P_2$:
  $\frac{1}{40320}\cdot t^{24}-\frac{155732067035034049359598960356799307}{14141280335882096837844848180608194890}\cdot t^{23}+\frac{6260340637331624116817606009725167688241}{2799973506504655173893279939760422588220}\cdot t^{22}-\frac{192996600347538464191787108002167308711123}{699993376626163793473319984940105647055}\cdot t^{21}+\frac{1028263042706509048615056990097008604604069}{44444023912772304347512379996197183940}\cdot t^{20}-\frac{9352118843280422563401795267012523862478556}{6666603586915845652126856999429577591}\cdot t^{19}+\frac{141553089162577169187670365890960648756497262}{2222201195638615217375618999809859197}\cdot t^{18}-\frac{4923229169993216704139591583786566038602402952}{2222201195638615217375618999809859197}\cdot t^{17}+\frac{399118336413338821035599207673700083349410160307}{6666603586915845652126856999429577591}\cdot t^{16}-\frac{8451908860636909156929714533564131816103617025792}{6666603586915845652126856999429577591}\cdot t^{15}+\frac{46952458554684894670271428110860925148035750218880}{2222201195638615217375618999809859197}\cdot t^{14}-\frac{616251569068439227950383637244178738959087481812480}{2222201195638615217375618999809859197}\cdot t^{13}+\frac{6354045886781612337717268356811730274787972729137280}{2222201195638615217375618999809859197}\cdot t^{12}-\frac{51180757722446397853741157994995112570770385317160960}{2222201195638615217375618999809859197}\cdot t^{11}+\frac{29019771498273965612286381356918602157467355450434560}{202018290512601383397783545437259927}\cdot t^{10}-\frac{138410019191496152674321351532828409766869359796940800}{202018290512601383397783545437259927}\cdot t^9+\frac{496357555489443363895018920345673670227703082297388800}{202018290512601383397783545437259927}\cdot t^8-\frac{1308570416587104781706639574561147927479079527302348800}{202018290512601383397783545437259927}\cdot t^7+\frac{2460913214586330438565162951581593642294772710405529600}{202018290512601383397783545437259927}\cdot t^6-\frac{3168594383199819189149117794284979887199889826769305600}{202018290512601383397783545437259927}\cdot t^5+\frac{2636183725736138022188288765151596440945047458571264000}{202018290512601383397783545437259927}\cdot t^4-\frac{1300423943961999636781612092681448137130881309425664000}{202018290512601383397783545437259927}\cdot t^3+\frac{331244480147378606346484670498253185809046621773824000}{202018290512601383397783545437259927}\cdot t^2-\frac{33835334957168856217297016108984754606116515381248000}{202018290512601383397783545437259927}\cdot t+\frac{759972077756134783743826706409852927404968194048000}{202018290512601383397783545437259927}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Laguerre type can be downloaded here packed into a single file.