Rule: Q[4, 19]

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.

• $P_1$:
  $\frac{1}{24}\cdot t^4-\frac{2}{3}\cdot t^3+3\cdot t^2-4\cdot t+1$
• $P_2$:
  $\frac{1}{24}\cdot t^{23}-\frac{490820724245111888642243025619357511858977}{26179518719845772174359062447427227906936}\cdot t^{22}+\frac{100452953628062933532648367198216047553054417}{26179518719845772174359062447427227906936}\cdot t^{21}-\frac{1379226132797374945298515034105261590326944265}{2908835413316196908262118049714136434104}\cdot t^{20}+\frac{216009037524078659333978014424147579271279584546}{5454066399967869202991471343214005813945}\cdot t^{19}-\frac{12940354307940011399367169508520689879075778011456}{5454066399967869202991471343214005813945}\cdot t^{18}+\frac{191923239557325931620018479502082584059763982038699}{1818022133322623067663823781071335271315}\cdot t^{17}-\frac{6481712693922755077337832765050686923099698059459887}{1818022133322623067663823781071335271315}\cdot t^{16}+\frac{168406196416858205381491022472986885182340295890530368}{1818022133322623067663823781071335271315}\cdot t^{15}-\frac{678481377841294204009768486431123641170713976592085312}{363604426664524613532764756214267054263}\cdot t^{14}+\frac{10633628214749839657054973339173763327940783817980633792}{363604426664524613532764756214267054263}\cdot t^{13}-\frac{129658246281011413408803906724371517569297664997094300864}{363604426664524613532764756214267054263}\cdot t^{12}+\frac{1226046455170208039942643993104609703853796898260856317952}{363604426664524613532764756214267054263}\cdot t^{11}-\frac{8934765468991167918471400263649408705283719618021570495488}{363604426664524613532764756214267054263}\cdot t^{10}+\frac{49705173715648999636121498140139900526299906492534934074880}{363604426664524613532764756214267054263}\cdot t^9-\frac{208315060656930071227648126153519515095365789617878608596480}{363604426664524613532764756214267054263}\cdot t^8+\frac{646106696340581244975015037884956851031296071161547051970560}{363604426664524613532764756214267054263}\cdot t^7-\frac{1448012887144750225245541823280963140453818242824200211066880}{363604426664524613532764756214267054263}\cdot t^6+\frac{2269809497689484953363862530790639499637910420669322017157120}{363604426664524613532764756214267054263}\cdot t^5-\frac{2377119266398113572098335319743382010274692519143675404595200}{363604426664524613532764756214267054263}\cdot t^4+\frac{1553306142535761557440294007745636135705689315428799943475200}{363604426664524613532764756214267054263}\cdot t^3-\frac{566020570325740947435598721025720867574705633481160140390400}{363604426664524613532764756214267054263}\cdot t^2+\frac{92692085644973304444091224096510872499359108869690950451200}{363604426664524613532764756214267054263}\cdot t-\frac{3911190411675692675520594165041435482774233340115246284800}{363604426664524613532764756214267054263}$

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.