Rule: Q[9, 17]

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.

• $P_1$:
  $\frac{-1}{362880}\cdot t^9+\frac{1}{4480}\cdot t^8-\frac{1}{140}\cdot t^7+\frac{7}{60}\cdot t^6-\frac{21}{20}\cdot t^5+\frac{21}{4}\cdot t^4-14\cdot t^3+18\cdot t^2-9\cdot t+1$
• $P_2$:
  $\frac{-1}{362880}\cdot t^{26}+\frac{2058476616986989891778961873293153744222888713}{1462004536198944252202192918325526032270835164160}\cdot t^{25}-\frac{483947713881177464788424184654308214376292163137}{1462004536198944252202192918325526032270835164160}\cdot t^{24}+\frac{7972963184476297939171374245344438293407921858101}{167521353106129028898167938558133191197699862560}\cdot t^{23}-\frac{785984893696456855796019682789770262060884601889383}{167521353106129028898167938558133191197699862560}\cdot t^{22}+\frac{56452880743875201502457346761502402770881447985969471}{167521353106129028898167938558133191197699862560}\cdot t^{21}-\frac{16214139188965361083750285391052131754405323665137167}{886356365640894332794539357450440165067195040}\cdot t^{20}+\frac{51081012672976108952094152900928744524067827122203947}{66476727423067074959590451808783012380039628}\cdot t^{19}-\frac{1686305988414687364136891031146689139735618105824292921}{66476727423067074959590451808783012380039628}\cdot t^{18}+\frac{8035063184507441678575651333372714697883022867092492511}{12086677713284922719925536692506002250916296}\cdot t^{17}-\frac{1849941692110474834322626043430780925031105712530543016437}{132953454846134149919180903617566024760079256}\cdot t^{16}+\frac{3876525786696846093653913999361666620368406211020421134032}{16619181855766768739897612952195753095009907}\cdot t^{15}-\frac{17352117731101045167219980311746390121808231487695399161040}{5539727285255589579965870984065251031669969}\cdot t^{14}+\frac{186215935153866207337723255161947514562128629195820765294320}{5539727285255589579965870984065251031669969}\cdot t^{13}-\frac{1589389667395133100190810962169873982513834888592560787171760}{5539727285255589579965870984065251031669969}\cdot t^{12}+\frac{10710187381316274678631161372124733992542224777528813056456320}{5539727285255589579965870984065251031669969}\cdot t^{11}-\frac{5127308240261221973095373662089519594820086595550101164965760}{503611571386871779996897362187750093788179}\cdot t^{10}+\frac{20816052540264095324162468767725301836056427584611425382490400}{503611571386871779996897362187750093788179}\cdot t^9-\frac{64006622865535557159950846636043545295178739952682786924999200}{503611571386871779996897362187750093788179}\cdot t^8+\frac{145646067282218019402542859707764814570473805216560442917401600}{503611571386871779996897362187750093788179}\cdot t^7-\frac{237851105300861822054925245168400812707357221988865145018547200}{503611571386871779996897362187750093788179}\cdot t^6+\frac{267436544962959707373721287889778909641023444234982737397017600}{503611571386871779996897362187750093788179}\cdot t^5-\frac{195301527792919038769235550788823373829730136019885038599552000}{503611571386871779996897362187750093788179}\cdot t^4+\frac{84906197811976466325369239973620436077457520371918608434176000}{503611571386871779996897362187750093788179}\cdot t^3-\frac{19038128833326684979434191409993203386503863612446648470528000}{503611571386871779996897362187750093788179}\cdot t^2+\frac{1661573115896110626932035557793259229715773950643628141056000}{503611571386871779996897362187750093788179}\cdot t-\frac{25526009055698495558231387204487995663537653589454801408000}{503611571386871779996897362187750093788179}$

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.