Rule: Q[2, 23]

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^{25}-\frac{117094862224969112525494618304870109673}{405532251666071461982930222261307442}\cdot t^{24}+\frac{652290940440620718643376723313873290655037}{8516177284987500701641534667487456282}\cdot t^{23}-\frac{105581275562171617436230163958409912024935757}{8516177284987500701641534667487456282}\cdot t^{22}+\frac{5841842147649615081887364520413583598616237685}{4258088642493750350820767333743728141}\cdot t^{21}-\frac{22349348264006310165893269449533678229032851603}{202766125833035730991465111130653721}\cdot t^{20}+\frac{1351269056798772563763006670214789332671342388780}{202766125833035730991465111130653721}\cdot t^{19}-\frac{62899264019462597865002425044241472756431603787420}{202766125833035730991465111130653721}\cdot t^{18}+\frac{2287292295242932456769945023851695204888473613310120}{202766125833035730991465111130653721}\cdot t^{17}-\frac{65568794310814330996874635945096780201782412146869400}{202766125833035730991465111130653721}\cdot t^{16}+\frac{1489008247842601169371004355608227955733254291215522560}{202766125833035730991465111130653721}\cdot t^{15}-\frac{26828125866456085173054842046899186666301694926401299200}{202766125833035730991465111130653721}\cdot t^{14}+\frac{382977825301505843286109326582968498414652212677876108800}{202766125833035730991465111130653721}\cdot t^{13}-\frac{4313652558978953529895032360968543221296913332030594316800}{202766125833035730991465111130653721}\cdot t^{12}+\frac{38070801077029454947942060876746365429458596936279331584000}{202766125833035730991465111130653721}\cdot t^{11}-\frac{260674465120050108119960083743041420770362085411235286374400}{202766125833035730991465111130653721}\cdot t^{10}+\frac{1366374527970748939732867358333540567282647085601420913152000}{202766125833035730991465111130653721}\cdot t^9-\frac{5388311782007936899503281293865833522191021754197788886528000}{202766125833035730991465111130653721}\cdot t^8+\frac{15632175383537392262548574181860783486965683325987935172608000}{202766125833035730991465111130653721}\cdot t^7-\frac{32415285867230021580699553100651608762369452044434515179520000}{202766125833035730991465111130653721}\cdot t^6+\frac{46279436754289222799665812282253533733004757569421063450624000}{202766125833035730991465111130653721}\cdot t^5-\frac{43288059764704478882077781629180292438128989414170127912960000}{202766125833035730991465111130653721}\cdot t^4+\frac{24757675242598837427790275705581499149208479909461176893440000}{202766125833035730991465111130653721}\cdot t^3-\frac{7785049417110866528782532319557004406864061140145223843840000}{202766125833035730991465111130653721}\cdot t^2+\frac{1101820331748363279843103045643637781976410480948948992000000}{202766125833035730991465111130653721}\cdot t-\frac{41102691230887578034539829622396008697823199892172472320000}{202766125833035730991465111130653721}$

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.