Rule: Q[4, 31]

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.

• $P_1$:
  $\frac{1}{24}\cdot t^4-\frac{2}{3}\cdot t^3+3\cdot t^2-4\cdot t+1$
• $P_2$:
  $\frac{1}{24}\cdot t^{35}-\frac{94097489629049189130811296665262401482097934589538489690407690979524481809806409490238836267}{2050660479259540254493591239887802794823465773172244530044394330552602914447509877994847912}\cdot t^{34}+\frac{170719805583369935315862928960948625197634062349050928190293758125751997863344767629808249938855}{7177311677408390890727569339607309781882130206102855855155380156934110200566284572981967692}\cdot t^{33}-\frac{18479652182331650091576738450868323355499854401203858465095418251006671522632486452324662561463487}{2392437225802796963575856446535769927294043402034285285051793385644703400188761524327322564}\cdot t^{32}+\frac{18995404879242748124109011018828899174596241439441072752673706014333456254540206855284196978915481199}{10765967516112586336091354009410964672823195309154283782733070235401165300849426859472951538}\cdot t^{31}-\frac{3248962038929901765429233668603317103278047520721592904925176647254106102548148307220490456881715290799}{10765967516112586336091354009410964672823195309154283782733070235401165300849426859472951538}\cdot t^{30}+\frac{24027507665028597446821276679601150855462574852716153289359414269282802268159169374575150466115212284695}{598109306450699240893964111633942481823510850508571321262948346411175850047190381081830641}\cdot t^{29}-\frac{7663689117228983051199798862855016294861906716443166923129789941083080148742815166313903012747215762168975}{1794327919352097722681892334901827445470532551525713963788845039233527550141571143245491923}\cdot t^{28}+\frac{94667827119979469646556697621697400656543730932481466938679604383800170731550143225850609233835521308786340}{256332559907442531811698904985975349352933221646530566255549291319075364305938734749355989}\cdot t^{27}-\frac{749497315214336263348024420937070521603060875254149669162593525695964476072689355897624280538325720365626260}{28481395545271392423522100553997261039214802405170062917283254591008373811770970527706221}\cdot t^{26}+\frac{44431718419510916630259640079084020068412941681420630910429431748131677670278779173313210578724255125672099960}{28481395545271392423522100553997261039214802405170062917283254591008373811770970527706221}\cdot t^{25}-\frac{2206840729750226252613843683983560790786772897468989988043058008468441170425326896483685342637348748393608605000}{28481395545271392423522100553997261039214802405170062917283254591008373811770970527706221}\cdot t^{24}+\frac{92295527546547538152982594315154224103687719053375497330168053366437698807277945032138086420364603791642703400000}{28481395545271392423522100553997261039214802405170062917283254591008373811770970527706221}\cdot t^{23}-\frac{3261395580061351730223822176017735686851707233757276909930289599375352045285572645467438006242870039449683041640000}{28481395545271392423522100553997261039214802405170062917283254591008373811770970527706221}\cdot t^{22}+\frac{97574817765917213357325364366406130419188655118615484690274287682037983076689460171362256512764387911357670759440000}{28481395545271392423522100553997261039214802405170062917283254591008373811770970527706221}\cdot t^{21}-\frac{2473843611640155142340766265876057050265123112557930665464801861166628806624307079004922857156919455936376427352240000}{28481395545271392423522100553997261039214802405170062917283254591008373811770970527706221}\cdot t^{20}+\frac{53141207946360384842735565591824376792792469608761998047562311100800443671047261089022690378365085909110969556571200000}{28481395545271392423522100553997261039214802405170062917283254591008373811770970527706221}\cdot t^{19}-\frac{50844596237249665051465186302959556622012797578513948561748152841164213303785276203900203274738387022745765178840000000}{1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959}\cdot t^{18}+\frac{780486191196496850681935070496878400072502494586686522899723048300277928660737413008705953870690879178719143934518400000}{1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959}\cdot t^{17}-\frac{10084006751054566683494525866557769007339527561960065333620585242263454388111283525017035699160170466404751615923094400000}{1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959}\cdot t^{16}+\frac{109183797224579823157432643407303325544008213523241565425561240282871867708261075189101599713344432470018836784044390400000}{1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959}\cdot t^{15}-\frac{985171775660478265916087256465352370682950873605639115134437763297870301649211403326343414632504962131515654031106816000000}{1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959}\cdot t^{14}+\frac{7356119364474427000632722288136942947961843406220107002514487723424925658043776340808861549228928978093709184197342720000000}{1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959}\cdot t^{13}-\frac{45060358693887987363365310544695574866553994166857275393034713496582907719208248956727149554658137942432310414128480768000000}{1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959}\cdot t^{12}+\frac{224023630046892544498984869426891013273040614876983782996523562221124382033189676507140020029055107609138148315625269248000000}{1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959}\cdot t^{11}-\frac{892066357215897500111500557566698659044171602647950373086427540962508462792720276978752802963188675763324785395963840512000000}{1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959}\cdot t^{10}+\frac{2798773829914640173358837798314404012500836478165302446602909452722680333304480464236080701868780772974623541186256121856000000}{1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959}\cdot t^9-\frac{6777428829971632751831707332961547993533370691394585291986853222030681671209751984168586106084320979524097795400150896640000000}{1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959}\cdot t^8+\frac{12340705319674522698878116635254609091546732134590735607618596121731043881030245296105673558867724678683783650204767715328000000}{1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959}\cdot t^7-\frac{16335434932852523263943205869961891640090360219300307560491090398797563565785848186650651187610116575765258478702426554368000000}{1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959}\cdot t^6+\frac{15032976389534025176865328545868642291312477954690556869076725495321548947603705568588844087679919390018310461709049069568000000}{1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959}\cdot t^5-\frac{9049454457703576485009612081872425848282942314573550681315016233345186481931578487758334475648458389198674804704342507520000000}{1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959}\cdot t^4+\frac{3267230060161173733899246267389754883318208439520661097361718536509512946710190708840382549129010675110233552839815987200000000}{1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959}\cdot t^3-\frac{620170343648784604457881869476968050434291169785585508564446346046681835741623553414158046572119850500144338645054914560000000}{1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959}\cdot t^2+\frac{49430499135478029953097926049457028855986670819715013157729296924049382915936922700044942865098474558777332208891330560000000}{1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959}\cdot t-\frac{984282964290848288897297207545795178775441699427126481329396647805514093070838164843362863069284919067500397930741760000000}{1499020818172178548606426344947224265221831705535266469330697610053072305882682659352959}$

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.