Rule: Q[1, 6, 12]

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.

• $P_1$:
  $-t+1$
• $P_2$:
  $-t^7+\frac{8861}{185}\cdot t^6-\frac{155826}{185}\cdot t^5+\frac{253590}{37}\cdot t^4-\frac{989880}{37}\cdot t^3+\frac{1737720}{37}\cdot t^2-\frac{1129104}{37}\cdot t+\frac{157104}{37}$
• $P_3$:
  $-t^{19}+\frac{37571100624534618675122865860210356801351620095847778626331337}{143130316232650652215404065089958306505962895112779976220345}\cdot t^{18}-\frac{875226064040284164985455714256860629359083096573612716414830080}{28626063246530130443080813017991661301192579022555995244069}\cdot t^{17}+\frac{299565191429079532824260940175271460861137507416300233427712101704}{143130316232650652215404065089958306505962895112779976220345}\cdot t^{16}-\frac{94210535691173414103129288466991141156367495916819962900249475107822}{1001912213628554565507828455629708145541740265789459833542415}\cdot t^{15}+\frac{587742623627195844093940021948762163947884426902480228650652607526950}{200382442725710913101565691125941629108348053157891966708483}\cdot t^{14}-\frac{13136175440283681920044844003632030586329217698168284586920096542868180}{200382442725710913101565691125941629108348053157891966708483}\cdot t^{13}+\frac{214085477617530434965602281553663103877538633454896475712147947134047100}{200382442725710913101565691125941629108348053157891966708483}\cdot t^{12}-\frac{69335914400491597452936657630071515631812602661453069084981553700116880}{5415741695289484137880153814214638624549947382645728829959}\cdot t^{11}+\frac{22634722122690342138340160780863434214035391038674330992595038235948753040}{200382442725710913101565691125941629108348053157891966708483}\cdot t^{10}-\frac{146346473452579481094861481294708716304546428090531400055203286197871383200}{200382442725710913101565691125941629108348053157891966708483}\cdot t^9+\frac{685971982433966633864530083130727501721908033873410218548983411793943750240}{200382442725710913101565691125941629108348053157891966708483}\cdot t^8-\frac{327211343623042644695936792381215657312746616408160435092888396993423507200}{28626063246530130443080813017991661301192579022555995244069}\cdot t^7+\frac{758307374725405821477742527324046998617316885238950837879584191032913616640}{28626063246530130443080813017991661301192579022555995244069}\cdot t^6-\frac{1174656591523216862133246735405182506522357835865003832870090511911980956160}{28626063246530130443080813017991661301192579022555995244069}\cdot t^5+\frac{1150993438407588619170517394541875008006120585966701407415071922386637504000}{28626063246530130443080813017991661301192579022555995244069}\cdot t^4-\frac{655687717197596955386686201321440214266639095917263458899958020334324889600}{28626063246530130443080813017991661301192579022555995244069}\cdot t^3+\frac{188793112646422919539290390306976623545570104830176769115571555169525504000}{28626063246530130443080813017991661301192579022555995244069}\cdot t^2-\frac{20954272076136125279128215477294838205165190728305027714041731311165747200}{28626063246530130443080813017991661301192579022555995244069}\cdot t+\frac{430809942393780703545072899294149468995156324655805043254104593186508800}{28626063246530130443080813017991661301192579022555995244069}$

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.