Rule: Q[2, 30]

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.

• $P_1$:
  $\frac{1}{2}\cdot t^2-2\cdot t+1$
• $P_2$:
  $\frac{1}{2}\cdot t^{32}-\frac{4274729692139483358921175620974382372407278704248767447}{8839866537711680468484631375864425900454364529026411}\cdot t^{31}+\frac{4172560193624610153286185255038909271108540047346169873991}{19039712542763619470582282963400301939440169754826116}\cdot t^{30}-\frac{3831462651689468890886756742341999484244765891264109714247225}{61879065763981763279392419631050981303180551703184877}\cdot t^{29}+\frac{1515088994211587300028196854188374229083950388273253943086463675}{123758131527963526558784839262101962606361103406369754}\cdot t^{28}-\frac{15932832943016267593855308264730697709855745423295962754633300160}{8839866537711680468484631375864425900454364529026411}\cdot t^{27}+\frac{1814744063044247350980361775734386876106496798846586836699234400990}{8839866537711680468484631375864425900454364529026411}\cdot t^{26}-\frac{12617039943682129524096882668884967161250652237393222098981157615240}{679989733670129266806510105835725069265720348386647}\cdot t^{25}+\frac{920997807102666427578972507238711002729004419080067078541260421612500}{679989733670129266806510105835725069265720348386647}\cdot t^{24}-\frac{54980759292980627127265775883835231932021803145347772958319057329200000}{679989733670129266806510105835725069265720348386647}\cdot t^{23}+\frac{2708263037719586412586596137162585209244705592244773510337876737141180000}{679989733670129266806510105835725069265720348386647}\cdot t^{22}-\frac{110768802719938931474459480366141308802309255067424578800058232254394320000}{679989733670129266806510105835725069265720348386647}\cdot t^{21}+\frac{3777492167285611265628905232051525500211321168995010269470921394774747160000}{679989733670129266806510105835725069265720348386647}\cdot t^{20}-\frac{107676225660804240953233351987058384262401756260346761905313561914909408000000}{679989733670129266806510105835725069265720348386647}\cdot t^{19}+\frac{2568026261561736460250795277802616641538596262896074859606458852131777052000000}{679989733670129266806510105835725069265720348386647}\cdot t^{18}-\frac{51227441409396754167805476541504164241610190192427630661886085717249158403200000}{679989733670129266806510105835725069265720348386647}\cdot t^{17}+\frac{853395391984192293242654585207830618311355922216584158907877442852785170228800000}{679989733670129266806510105835725069265720348386647}\cdot t^{16}-\frac{11839467527969155662710245995902883204338430758648227338663754991648068616294400000}{679989733670129266806510105835725069265720348386647}\cdot t^{15}+\frac{136235935264424888867497314617167929420105985204785532655266830014465144964480000000}{679989733670129266806510105835725069265720348386647}\cdot t^{14}-\frac{1293258610327958499645977942933426408378250585845763971897931203639115400081920000000}{679989733670129266806510105835725069265720348386647}\cdot t^{13}+\frac{10058037800390587033405104554589668158761166282369986631177167386184344931988224000000}{679989733670129266806510105835725069265720348386647}\cdot t^{12}-\frac{63534713122192872357998701666170146223006899050337258380552024294623122441158656000000}{679989733670129266806510105835725069265720348386647}\cdot t^{11}+\frac{322470676517648806843179261471931762689807793083093457081621023607015441474556928000000}{679989733670129266806510105835725069265720348386647}\cdot t^{10}-\frac{1297482497242523703836560280049433243255661312407879333162145887994422789476249600000000}{679989733670129266806510105835725069265720348386647}\cdot t^9+\frac{4068955991491469996380654910609095248964708434458317838430136189630097549464934400000000}{679989733670129266806510105835725069265720348386647}\cdot t^8-\frac{9732516751834734695390521250759543714861955786149072462646736015042029669449662464000000}{679989733670129266806510105835725069265720348386647}\cdot t^7+\frac{17259716685931955632334028002421779225347122912675356828406439479649957067196973056000000}{679989733670129266806510105835725069265720348386647}\cdot t^6-\frac{21845527105419309510032662169951321103718005776575157449195300965575268022417686528000000}{679989733670129266806510105835725069265720348386647}\cdot t^5+\frac{18708734203490799775137000642878715522832581696990541613182824716598717118731878400000000}{679989733670129266806510105835725069265720348386647}\cdot t^4-\frac{10018581866361461194158147612535743750095051423183853814737425676804184667298201600000000}{679989733670129266806510105835725069265720348386647}\cdot t^3+\frac{2955272475048993242068294429096775820455082922444818821771221520621831989259796480000000}{679989733670129266806510105835725069265720348386647}\cdot t^2-\frac{380091847804156234985857912035837236982014523929500568065526232565891014100254720000000}{679989733670129266806510105835725069265720348386647}\cdot t+\frac{12003599178258431836547409077837142836673807826538660833189709872309377057423360000000}{679989733670129266806510105835725069265720348386647}$

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.