Rule: Q[7, 15]

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.

• $P_1$:
  $\frac{-1}{5040}\cdot t^7+\frac{7}{720}\cdot t^6-\frac{7}{40}\cdot t^5+\frac{35}{24}\cdot t^4-\frac{35}{6}\cdot t^3+\frac{21}{2}\cdot t^2-7\cdot t+1$
• $P_2$:
  $\frac{-1}{5040}\cdot t^{22}+\frac{20537853706984048056173384256728419}{272049232864620213787750558614030240}\cdot t^{21}-\frac{56300057947779891974744925925866459}{4318241791501908155361119978000480}\cdot t^{20}+\frac{3514996909267063911886297040692665695}{2590945074901144893216671986800288}\cdot t^{19}-\frac{246703740692178869049659769733530041555}{2590945074901144893216671986800288}\cdot t^{18}+\frac{2064897990882605584281502545187025962099}{431824179150190815536111997800048}\cdot t^{17}-\frac{230435840353488967221891918594314198150423}{1295472537450572446608335993400144}\cdot t^{16}+\frac{589543718147106850034264282951152443567649}{117770230677324767873485090309104}\cdot t^{15}-\frac{46604409195673882408038078554309072639259225}{431824179150190815536111997800048}\cdot t^{14}+\frac{387366844971787692023000880529594748386706825}{215912089575095407768055998900024}\cdot t^{13}-\frac{4973336693655201865516194683316418731529029755}{215912089575095407768055998900024}\cdot t^{12}+\frac{12297123459637092302062258568020626912797373555}{53978022393773851942013999725006}\cdot t^{11}-\frac{8461695757226381708801212662590233734504499965}{4907092944888531994728545429546}\cdot t^{10}+\frac{24244311016921840445657373481511486283698838375}{2453546472444265997364272714773}\cdot t^9-\frac{103547790753039606423150391591061974866608816625}{2453546472444265997364272714773}\cdot t^8+\frac{322596237766683144680129243812681049886286014600}{2453546472444265997364272714773}\cdot t^7-\frac{711875009607663940188915065885805238835067923400}{2453546472444265997364272714773}\cdot t^6+\frac{1068544127658935656117491535243490731957330261200}{2453546472444265997364272714773}\cdot t^5-\frac{1030085044444491435106697780010302169005427510000}{2453546472444265997364272714773}\cdot t^4+\frac{585257625530959288123976254872939357628964040000}{2453546472444265997364272714773}\cdot t^3-\frac{170421464738964179177823246665326840308063528000}{2453546472444265997364272714773}\cdot t^2+\frac{19554189481592882480117430428299376101810992000}{2453546472444265997364272714773}\cdot t-\frac{456347372365474366645657007685199489903056000}{2453546472444265997364272714773}$

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.