Rule: Q[1, 7, 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.

• $P_1$:
  $-t+1$
• $P_2$:
  $-t^8+\frac{19265}{204}\cdot t^7-\frac{624113}{204}\cdot t^6+\frac{1552467}{34}\cdot t^5-\frac{11604425}{34}\cdot t^4+\frac{21609490}{17}\cdot t^3-\frac{36977850}{17}\cdot t^2+\frac{23737980}{17}\cdot t-\frac{3293220}{17}$
• $P_3$:
  $-t^{20}+\frac{1226775058853916143304149911520559664174311340375636600318183687283}{3945885944626245244193056853752619996849064308586889189222119012}\cdot t^{19}-\frac{851566068806410647916174730688595191154291245079213807641749165657467}{19729429723131226220965284268763099984245321542934445946110595060}\cdot t^{18}+\frac{1166049086647473882505056089659417695355289019047019400382691275185488}{328823828718853770349421404479384999737422025715574099101843251}\cdot t^{17}-\frac{316769274727203555164878603611359051354250597733848931931800666638465192}{1644119143594268851747107022396924998687110128577870495509216255}\cdot t^{16}+\frac{24100575028201223411225888747498508011972767301345858631102337946158521981}{3288238287188537703494214044793849997374220257155740991018432510}\cdot t^{15}-\frac{132622093850308686445957212757219433736427954616665534923070862294291527725}{657647657437707540698842808958769999474844051431148198203686502}\cdot t^{14}+\frac{79094412753961599222183142236405622609405941196835716083027169585548667935}{19342578159932574726436553204669705866907177983269064653049603}\cdot t^{13}-\frac{20293134405698950516334455894883460827334024820715374510548804091238197655625}{328823828718853770349421404479384999737422025715574099101843251}\cdot t^{12}+\frac{844004155241081081130195464342186577799786977261400025067453068344364337540}{1213372061693187344462809610625036899400081275703225457940381}\cdot t^{11}-\frac{1921305856000439225197007159240405257895232159934549144631179303924040973007260}{328823828718853770349421404479384999737422025715574099101843251}\cdot t^{10}+\frac{11942187128366957504109375076977363194170896667439102400257309440985825307665400}{328823828718853770349421404479384999737422025715574099101843251}\cdot t^9-\frac{54239168944282392048230673048483274388019497374937727420131346196341440459390760}{328823828718853770349421404479384999737422025715574099101843251}\cdot t^8+\frac{176629590218146828095432661699061301781020461297038617655842865099198932159864000}{328823828718853770349421404479384999737422025715574099101843251}\cdot t^7-\frac{401395262047064583702686967318935526494370087265300389705369058078411376559030720}{328823828718853770349421404479384999737422025715574099101843251}\cdot t^6+\frac{612555388741629106313204231038549534103272659780652442349689658879142851487946880}{328823828718853770349421404479384999737422025715574099101843251}\cdot t^5-\frac{593932864804844858779466277796365053905676257824653378568781506866108916112560000}{328823828718853770349421404479384999737422025715574099101843251}\cdot t^4+\frac{337192894992695719530277154109098033821912889630641140006478199656606168397452800}{328823828718853770349421404479384999737422025715574099101843251}\cdot t^3-\frac{99273581795281112317434492743485131819741891546125583325867627074835161845184000}{328823828718853770349421404479384999737422025715574099101843251}\cdot t^2+\frac{12745939512776749329924745210070967437243670100824562408127552289509372721945600}{328823828718853770349421404479384999737422025715574099101843251}\cdot t-\frac{30207634096006294776058310930141768294490127913769104133627268508373921715200}{19342578159932574726436553204669705866907177983269064653049603}$

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.