Rule: Q[1, 3, 5, 9]

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.

• $P_1$:
  $-t+1$
• $P_2$:
  $-t^4+\frac{49}{4}\cdot t^3-\frac{153}{4}\cdot t^2+\frac{57}{2}\cdot t-\frac{3}{2}$
• $P_3$:
  $-t^9+\frac{8913807221}{174577516}\cdot t^8-\frac{346896933499}{349155032}\cdot t^7+\frac{3329250396937}{349155032}\cdot t^6-\frac{8538378231899}{174577516}\cdot t^5+\frac{23551735187795}{174577516}\cdot t^4-\frac{8100489458905}{43644379}\cdot t^3+\frac{4370729197935}{43644379}\cdot t^2-\frac{409117906830}{43644379}\cdot t+\frac{10559938470}{43644379}$
• $P_4$:
  $-t^{18}+\frac{22708488691319527480486427375172231919735172902478723844140662903702170011930260041442943255346869444966911444214616807754079}{104106150389261141065797045765771918737707979083496765317286803200986229290626990010714616465305315381354066951107698014830}\cdot t^{17}-\frac{3487095950379061336077076152512905324317506169767200347275531601852602027545931183351592857799775816583621219141700581993739365}{166569840622817825705275273225235069980332766533594824507658885121577966865003184017143386344488504610166507121772316823728}\cdot t^{16}+\frac{1949039484103399929557957398468735520241576005178732499314803035057696387010796582813231156026771547251439288185009988517113816377}{1665698406228178257052752732252350699803327665335948245076588851215779668650031840171433863444885046101665071217723168237280}\cdot t^{15}-\frac{70791931553222209656799581487769530425417587565295405734444196344798211539584953379007518567443325785965664928255712511635801644399}{1665698406228178257052752732252350699803327665335948245076588851215779668650031840171433863444885046101665071217723168237280}\cdot t^{14}+\frac{4415031598807143415721605153062015398975998182582646458045827663535844692865522025604910685675529269570311185139558005001383936888821}{4164246015570445642631881830630876749508319163339870612691472128039449171625079600428584658612212615254162678044307920593200}\cdot t^{13}-\frac{939533995247230237309316929725029781765234819005931945407099002217156786024369054978858060437869747453946829932263427384666366784891}{50171638741812598103998576272661165656726736907709284490258700337824688814759995185886562151954368858483887687280818320400}\cdot t^{12}+\frac{247778093862505356260224667311358194567036127980625374503344759016238378903092853743528493953314949100737712941865472230252307079025947}{1041061503892611410657970457657719187377079790834967653172868032009862292906269900107146164653053153813540669511076980148300}\cdot t^{11}-\frac{2281130617064803176983608514108918171005000097109434555205291134177380168055432754594940017849821624110244871750045303868976891058794049}{1041061503892611410657970457657719187377079790834967653172868032009862292906269900107146164653053153813540669511076980148300}\cdot t^{10}+\frac{37995875058487480000042185533043716802753590525614386725150600751702873370218451043381145267381890452135937276151703151844000019404231921}{2602653759731528526644926144144297968442699477087419132932170080024655732265674750267865411632632884533851673777692450370750}\cdot t^9-\frac{181751555914150330824849103158510363356483508369003564617052336203233102369095336333964115853182329382061006618906734151984405069652441401}{2602653759731528526644926144144297968442699477087419132932170080024655732265674750267865411632632884533851673777692450370750}\cdot t^8+\frac{307176869318664702885415369197693402406751485051062102621061669236747659420189887534223669591603719856472919548567295477134385812272486316}{1301326879865764263322463072072148984221349738543709566466085040012327866132837375133932705816316442266925836888846225185375}\cdot t^7-\frac{714686542005189514783672462782729300188221767641283212851481226285099474675307202221569913366298371001456248147752769474021264503801817428}{1301326879865764263322463072072148984221349738543709566466085040012327866132837375133932705816316442266925836888846225185375}\cdot t^6+\frac{1097756178496754434691135148194377314380677789430653900004932757721005955507646145496867241545579996700515874283229793399960947060578912952}{1301326879865764263322463072072148984221349738543709566466085040012327866132837375133932705816316442266925836888846225185375}\cdot t^5-\frac{208256046363298550486857159823303513807720778077526005616609904852534409199958113632306071763983862876984986665703716676960849007868330552}{260265375973152852664492614414429796844269947708741913293217008002465573226567475026786541163263288453385167377769245037075}\cdot t^4+\frac{109230282886681199931715893462627212933382609049750689903064964702069691583270239871471424594705643212397509515349122941528800981007106272}{260265375973152852664492614414429796844269947708741913293217008002465573226567475026786541163263288453385167377769245037075}\cdot t^3-\frac{26087496593283263907612260816218676134949725958137092279306238698049569766032936786262948480858762155566314963125817549086812306403816864}{260265375973152852664492614414429796844269947708741913293217008002465573226567475026786541163263288453385167377769245037075}\cdot t^2+\frac{1999871075886795873125798382491623507212777305434481515544190526023395546545177733148818649479420890222126233412222722696119778261133632}{260265375973152852664492614414429796844269947708741913293217008002465573226567475026786541163263288453385167377769245037075}\cdot t-\frac{47397296445864604964807368692349086526327402254913540483864747362933022021232226042252297978979588142844725846224344201088473618762048}{260265375973152852664492614414429796844269947708741913293217008002465573226567475026786541163263288453385167377769245037075}$

Warning: This rule has negative weights!

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.