Rule: Q[2, 29]

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^{31}-\frac{48614546813951848684734013700167045133324599234513837}{106720709441450512511536498964253521024741026692238}\cdot t^{30}+\frac{279657703162504138571296151981462547693862749138882970463}{1440729577459581918905742736017422533834003860345213}\cdot t^{29}-\frac{74146693988605806702618146645630324691036376736841408274583}{1440729577459581918905742736017422533834003860345213}\cdot t^{28}+\frac{13727789470020430188439849881232758886147134024031988488573036}{1440729577459581918905742736017422533834003860345213}\cdot t^{27}-\frac{69935389546999969544541139361194735917602875985201817936057564}{53360354720725256255768249482126760512370513346119}\cdot t^{26}+\frac{7423926656247583994497575663021281171391223257247114380718185576}{53360354720725256255768249482126760512370513346119}\cdot t^{25}-\frac{623714769233677857507555942207324400031769109728945578233476357000}{53360354720725256255768249482126760512370513346119}\cdot t^{24}+\frac{42199865355883846697867920952979835116066619346682641403981864072000}{53360354720725256255768249482126760512370513346119}\cdot t^{23}-\frac{2327743929340771793395649480352866347186375953691862830649862514584000}{53360354720725256255768249482126760512370513346119}\cdot t^{22}+\frac{105587008722722000436381612151860299554781252063998838581565767498992000}{53360354720725256255768249482126760512370513346119}\cdot t^{21}-\frac{3961970465687924853166690410568547794620853565714557511903749702276848000}{53360354720725256255768249482126760512370513346119}\cdot t^{20}+\frac{123447607130186312254915186182710973855749860890577368036167137061382720000}{53360354720725256255768249482126760512370513346119}\cdot t^{19}-\frac{3200359797245478450461945120028968908720033651553986252718008079895222720000}{53360354720725256255768249482126760512370513346119}\cdot t^{18}+\frac{69065379607102261746218305491136737549793125908942930174771046038737933440000}{53360354720725256255768249482126760512370513346119}\cdot t^{17}-\frac{1239511132487646307895525755445099934873654785910869776134454499269401774720000}{53360354720725256255768249482126760512370513346119}\cdot t^{16}+\frac{18456786725416193606555285877183068291651247530514874610502002460235516692480000}{53360354720725256255768249482126760512370513346119}\cdot t^{15}-\frac{227175619902233143168873028068043289216633624017907553926991930693899862579200000}{53360354720725256255768249482126760512370513346119}\cdot t^{14}+\frac{2299391071416481437319847843329749340100851223315672261847279439253444641075200000}{53360354720725256255768249482126760512370513346119}\cdot t^{13}-\frac{19008511949059169268723506184365755122148858436083019332982333087892242760806400000}{53360354720725256255768249482126760512370513346119}\cdot t^{12}+\frac{127230643697462499095897602287533435570023845334979422953669101007478827920179200000}{53360354720725256255768249482126760512370513346119}\cdot t^{11}-\frac{682013146741572764950005255686240625588817537606916751530310838246886948377804800000}{53360354720725256255768249482126760512370513346119}\cdot t^{10}+\frac{2887948093627823655184290057506053714846955515617695077299114227275061711253504000000}{53360354720725256255768249482126760512370513346119}\cdot t^9-\frac{9494242968650448323246853531083903191719846535699216043575740916554269486444544000000}{53360354720725256255768249482126760512370513346119}\cdot t^8+\frac{23702749968293937761099086080719636114510276201924836670895535399824429269680128000000}{53360354720725256255768249482126760512370513346119}\cdot t^7-\frac{43660775061576081833657225341399462686179625478506827188787391416751921431150592000000}{53360354720725256255768249482126760512370513346119}\cdot t^6+\frac{57092398090116324971832836758198331613148869592786630794349336555123987435683840000000}{53360354720725256255768249482126760512370513346119}\cdot t^5-\frac{50224693096213559764641468807831389599645917570029784226089706413891568186884096000000}{53360354720725256255768249482126760512370513346119}\cdot t^4+\frac{27462535563953924965040622253207713690497085573630394791267698575694421155905536000000}{53360354720725256255768249482126760512370513346119}\cdot t^3-\frac{8222819229228759587220822002711390137178090618780700881495326551445430946496512000000}{53360354720725256255768249482126760512370513346119}\cdot t^2+\frac{1067564295879613084894512887275473715352880818352955306023177845598764074008576000000}{53360354720725256255768249482126760512370513346119}\cdot t-\frac{33869225093679017944504819427545432784239469084769138095875331324981958672384000000}{53360354720725256255768249482126760512370513346119}$

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.