Rule: Q[3, 37]

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.

• $P_1$:
  $\frac{-1}{6}\cdot t^3+\frac{3}{2}\cdot t^2-3\cdot t+1$
• $P_2$:
  $\frac{-1}{6}\cdot t^{40}+\frac{8148763327054863743494950442836706903698900446327970969848437724691811984841145853766113031152202641}{27066379837767945636124854807435125048119820632224435394180682521055983598797236795516229308029820}\cdot t^{39}-\frac{2273511908275836381682766498769994451885926153862875775025596579788266823400188818831921974484627902817}{9022126612589315212041618269145041682706606877408145131393560840351994532932412265172076436009940}\cdot t^{38}+\frac{10041007457766770835514974141727020940284073059528199112951976886112516413274001292599998584115154689285147}{76688076207009179302353755287732854303006158457969233616845267142991953529925504253962649706084490}\cdot t^{37}-\frac{3653195763332514256639588156466239949503077208432663170796696215018354666936380846016491457662906404683124379}{76688076207009179302353755287732854303006158457969233616845267142991953529925504253962649706084490}\cdot t^{36}+\frac{497024292850909570846562037944636005213475121446482980912073277468618371043246982087065296057195981661044037682}{38344038103504589651176877643866427151503079228984616808422633571495976764962752126981324853042245}\cdot t^{35}-\frac{430241268559438195784665769892556919279743756777502263598875529071564511129212912899397949528066624228010669174}{156506277973488121025211745485169090414298282567284150238459728863248884754950008681556427971601}\cdot t^{34}+\frac{4302247519076631391701288418329557932434597648091305639270570129842979337694781752383582833042418728598886076972}{9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153}\cdot t^{33}-\frac{4186424049357716234864470733986522250460430008840995364932052217538835003312056507462384415938145896632154701867044}{64443761518495108657440130493893154876475763410058179509954006002514246663802944751229117400071}\cdot t^{32}+\frac{482971151893964691940586223172016403418039779805861547987626881779570804536675664892985715291683775780987104718734848}{64443761518495108657440130493893154876475763410058179509954006002514246663802944751229117400071}\cdot t^{31}-\frac{46758329939951663040723919525656585517942216662767344339688404928886969837598626035410363973379198821934077234724684288}{64443761518495108657440130493893154876475763410058179509954006002514246663802944751229117400071}\cdot t^{30}+\frac{3831232906817086784018393461512522900545582818678283478888332571097695552755463836684483640031523491882029002223205309440}{64443761518495108657440130493893154876475763410058179509954006002514246663802944751229117400071}\cdot t^{29}-\frac{267405341016161728512321786271122362694775421547456501732255341963362287411942175797229211610655152078691079507625036119040}{64443761518495108657440130493893154876475763410058179509954006002514246663802944751229117400071}\cdot t^{28}+\frac{2282341152461768587093337189270780656987201014379206660817028179980615837628831639259530089652840865575266953344945032990720}{9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153}\cdot t^{27}-\frac{117147887808024895358332043177090729969664722347666090019899240444126475524339311464602968126375758947275382290251429204029440}{9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153}\cdot t^{26}+\frac{5178873596274173981584225937849878851980486870337022850477702067547171467307351683421016273297313917776238745459687300166410240}{9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153}\cdot t^{25}-\frac{197506281629379525219708379878610539026430912182180114628307424076736693663637219581223905853464437869397369683799062317624320000}{9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153}\cdot t^{24}+\frac{6502928195896254992140066421277369079252084030109680700932242436653745348349633674881396190393398380259852319567845691880017920000}{9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153}\cdot t^{23}-\frac{184852780549841021913823121436532184511376939800244632404383125236239836479469906416218479596978948845819603938731348199469854720000}{9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153}\cdot t^{22}+\frac{4533406476311432672632569644480277292191148157367594945113961713397937989335810316918031359296071080288446523094420451559887216640000}{9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153}\cdot t^{21}-\frac{95783604078968125742219464955639286974852228536085208447300310729405552762535750947229596115486165853754148410959904752036050903040000}{9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153}\cdot t^{20}+\frac{1739817912247697316397717574974021677841904345427680989989800574461302703009301533920193678049687820486829088567873181070270253465600000}{9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153}\cdot t^{19}-\frac{27090863491262335977760859778132117781112912914407260928759115206211410324575761400585202884779103742770960315912236393896936040857600000}{9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153}\cdot t^{18}+\frac{360306264338615759161941487260679851380286528193454455728539057019838328422817767264051637010198362610073959178658044550770718161305600000}{9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153}\cdot t^{17}-\frac{4074822780772494784093336879792160241592616764386231810360571767515013783160818246505610944539703995710466724601933423553017185522483200000}{9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153}\cdot t^{16}+\frac{38975005092716478588387497064274986322975193301621800849667176779372580954028682284590245797847199987502239254219482929479746523181875200000}{9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153}\cdot t^{15}-\frac{313254627783132631495064621653153623601372387419793418629626098028704263920434630640738007120259120352746381347565125789715442455386521600000}{9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153}\cdot t^{14}+\frac{2099448740964660345126868923995946570422256956386418349937678064731164378803774022996167266626379841041579109937497651101184145427110297600000}{9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153}\cdot t^{13}-\frac{11626442468458204239517932802818708417636766169588879229021601639133946345973668237406683217068638583573799595330193286332813965432822169600000}{9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153}\cdot t^{12}+\frac{52626957946889334953219162375333771646105922026617200559352489728310576087121396340401784276988429047821246405350856689136143321275773747200000}{9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153}\cdot t^{11}-\frac{192200360008199232107300788111972625890673351132828270901716915483699323980538968596833169417794303704483568671454485003249928159725040435200000}{9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153}\cdot t^{10}+\frac{557562433672975098167503609125445982889961476670014992418707998329764938579011650838627426586385452500770057944666950427550298891551244288000000}{9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153}\cdot t^9-\frac{1260512967236050289905257578262462767242009145756791180176360648382754224643634269289760503965873119750174600924295063592210808364322521088000000}{9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153}\cdot t^8+\frac{2169010315574555755048539971627061273461718058546536778301322721787843157297669233828890063721260556842695265621824757113664818296251219968000000}{9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153}\cdot t^7-\frac{2757130040173329590402276325772509787143765530862872862036443427122560819174862020154902409568101423579328927686552530042194426445279789056000000}{9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153}\cdot t^6+\frac{2490028052962415682410134842928481151730065351621711049093374120744379119185039843661764888088452826949985852795014502538784378576422567936000000}{9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153}\cdot t^5-\frac{1515159810200614467896931230750882321328711899706885140056854447831899084295331636156058334728986649803328256972931960414769910917030215680000000}{9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153}\cdot t^4+\frac{575235466954992595717133023085664872796896464178562916467536185697227802664792339901411934654637962894721830326626693133004665191797882880000000}{9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153}\cdot t^3-\frac{120580560979983871802951313687557729390660929170209488201042467538065851873660734557034751273884169732036233253901399681144416784749690880000000}{9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153}\cdot t^2+\frac{11128413564917128354275472347326575202043217660100243666625545339589098869228574540281978897721045212899737357424130858375599793907957760000000}{9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153}\cdot t-\frac{257191607956165021276410726824683546309504642050741990951457227013931294452444360726711831874662848504170302217688180201095462607912960000000}{9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153}$

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.