Rule: Q[2, 27]

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.

• $P_1$:
  $\frac{1}{2}\cdot t^2-2\cdot t+1$
• $P_2$:
  $\frac{1}{2}\cdot t^{29}-\frac{616772358982709116157490999324063452976243194053}{1550562711749803401852393689194704654275504354}\cdot t^{28}+\frac{5709543934014672309445511303114050627987805002029179}{38764067793745085046309842229867616356887608850}\cdot t^{27}-\frac{1308612913412918501735958126973166180632587211378688691}{38764067793745085046309842229867616356887608850}\cdot t^{26}+\frac{104134665727984303430941612219502988815537434382854442079}{19382033896872542523154921114933808178443804425}\cdot t^{25}-\frac{489537720014341719843794289066518491130195195366159450325}{775281355874901700926196844597352327137752177}\cdot t^{24}+\frac{44110284483860992804867295285104641837580048047663138406800}{775281355874901700926196844597352327137752177}\cdot t^{23}-\frac{3123263582558882886695334894910720050801900455101525144053840}{775281355874901700926196844597352327137752177}\cdot t^{22}+\frac{176713562646996747694200786181842405173064352781631852625721760}{775281355874901700926196844597352327137752177}\cdot t^{21}-\frac{197127859413834169946004442548957691621209090137671045349299680}{18909301362802480510395044990179325052140297}\cdot t^{20}+\frac{301149915571555572396774046430151683982819685087285101261214824000}{775281355874901700926196844597352327137752177}\cdot t^{19}-\frac{9187097571673141616337962732238540974125931202580081931268472296000}{775281355874901700926196844597352327137752177}\cdot t^{18}+\frac{230080350735618636456684690660087930344084662949039275306655406902400}{775281355874901700926196844597352327137752177}\cdot t^{17}-\frac{4733649964911068659172971296971129338654960383213608176754313740937600}{775281355874901700926196844597352327137752177}\cdot t^{16}+\frac{79922084424461846409966244542220861637382601624258175313914215297228800}{775281355874901700926196844597352327137752177}\cdot t^{15}-\frac{1104310014964950646670603097106218179295868328939177590299699460469760000}{775281355874901700926196844597352327137752177}\cdot t^{14}+\frac{12431407893078534126471955072577262689396668830740180775613238159216640000}{775281355874901700926196844597352327137752177}\cdot t^{13}-\frac{113294753267257743309724841346895218149068637553857749760971581523329024000}{775281355874901700926196844597352327137752177}\cdot t^{12}+\frac{828944199209655144915059646437238648360310976963673407478396103060924416000}{775281355874901700926196844597352327137752177}\cdot t^{11}-\frac{4817207907335310162149031531838192344681233397654572324438570192841566208000}{775281355874901700926196844597352327137752177}\cdot t^{10}+\frac{21932480938871936095300471600487869857983121100166178249200317498799001600000}{775281355874901700926196844597352327137752177}\cdot t^9-\frac{76890803098258757482091184061716052181049715691018190978376626618315878400000}{775281355874901700926196844597352327137752177}\cdot t^8+\frac{203012561664446319083509993747397653542806328968847308533980433294763950080000}{775281355874901700926196844597352327137752177}\cdot t^7-\frac{392192170575090799472948546652096178735738686742614915368878376513090027520000}{775281355874901700926196844597352327137752177}\cdot t^6+\frac{533403109761782315655244646016816780839488834971552250906878721383327989760000}{775281355874901700926196844597352327137752177}\cdot t^5-\frac{484102095712082021191290892917483952790088726712466902136664419717824512000000}{775281355874901700926196844597352327137752177}\cdot t^4+\frac{271006285362175578964653268110858943972558587899486970303184406014230528000000}{775281355874901700926196844597352327137752177}\cdot t^3-\frac{82513325900747117853139825498420979350860670942389851225622449548559646720000}{775281355874901700926196844597352327137752177}\cdot t^2+\frac{10833812333183961094235198792423543558394224856700937614164652455564410880000}{775281355874901700926196844597352327137752177}\cdot t-\frac{346332560338326875571777278403535917887764721494478454786462175332925440000}{775281355874901700926196844597352327137752177}$

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.