Rule: Q[1, 3, 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.

• $P_1$:
  $-t+1$
• $P_2$:
  $-t^4+\frac{49}{4}\cdot t^3-\frac{153}{4}\cdot t^2+\frac{57}{2}\cdot t-\frac{3}{2}$
• $P_3$:
  $-t^{23}+\frac{2967417930088458284793920705351744450134437385517518486007649977219}{6516696794286640554149519379353965622932972151062076330124068388}\cdot t^{22}-\frac{1229686618426373418405591750115990203393835737337757494933291553427943}{13033393588573281108299038758707931245865944302124152660248136776}\cdot t^{21}+\frac{102591227810103949316497086752565608921968483882954472019250772937882693}{8688929059048854072199359172471954163910629534749435106832091184}\cdot t^{20}-\frac{173612109082809906867474056365723517875360088178866561566927453212283977971}{173778581180977081443987183449439083278212590694988702136641823680}\cdot t^{19}+\frac{10537145889916617549701781997203552369445654465051600878473626514879511357131}{173778581180977081443987183449439083278212590694988702136641823680}\cdot t^{18}-\frac{237497270090730416900635635214580080644494865724467564390539510404655088084411}{86889290590488540721993591724719541639106295347494351068320911840}\cdot t^{17}+\frac{477893397154711492415990111444729864325580547974547070816938153349123728473929}{5111134740616972983646681866159973037594487961617314768724759520}\cdot t^{16}-\frac{392797899936864696523841703804651894608851010536452628994840823130909932087858}{159722960644280405738958808317499157424827748800541086522648735}\cdot t^{15}+\frac{1600460976863212326688812048626422191350968169038293617817260290178944009141122}{31944592128856081147791761663499831484965549760108217304529747}\cdot t^{14}-\frac{25328711086719656252436265461345516633898712635390513152076398654462218514654252}{31944592128856081147791761663499831484965549760108217304529747}\cdot t^{13}+\frac{311140239764754145814211126465869055757672202011374697419708713339057930589861684}{31944592128856081147791761663499831484965549760108217304529747}\cdot t^{12}-\frac{2954331488756585760718724027274410445920650081168238517230352536500269781371188712}{31944592128856081147791761663499831484965549760108217304529747}\cdot t^{11}+\frac{21520726336290364407799157769978492804449929427873125388280269122156495469633473128}{31944592128856081147791761663499831484965549760108217304529747}\cdot t^{10}-\frac{118944172133774533134540914678772742514770208562664776294451543727562623650180619280}{31944592128856081147791761663499831484965549760108217304529747}\cdot t^9+\frac{491321048218506520362979076129788598651852534638090320010259690746767180492354488880}{31944592128856081147791761663499831484965549760108217304529747}\cdot t^8-\frac{1486869467552972877686664738383033467397988598657171894910559856718880343412498223360}{31944592128856081147791761663499831484965549760108217304529747}\cdot t^7+\frac{3211786555569535566125012341478532233073901303580665527400932432787726513703557121280}{31944592128856081147791761663499831484965549760108217304529747}\cdot t^6-\frac{4784612329546696298890638669805476042044198601658611803314727766542442417807793374720}{31944592128856081147791761663499831484965549760108217304529747}\cdot t^5+\frac{4691057769678147436833494847041624642128008839193185156174111957556053821701920371200}{31944592128856081147791761663499831484965549760108217304529747}\cdot t^4-\frac{2829565114093491765099781138690384868457822426220384568390613515431222724130491251200}{31944592128856081147791761663499831484965549760108217304529747}\cdot t^3+\frac{941963074310698216091183004562275144493158130964800822461570521492641978641151142400}{31944592128856081147791761663499831484965549760108217304529747}\cdot t^2-\frac{140405140342986489484135310002946668807890609364541485254112518953062149063773107200}{31944592128856081147791761663499831484965549760108217304529747}\cdot t+\frac{5414044714001540986610493291587210206982928067800831229270622482164355855022668800}{31944592128856081147791761663499831484965549760108217304529747}$

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.