Rule: Q[8, 9, 18]

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.

• $P_1$:
  $\frac{6435}{128}\cdot t^8-\frac{3003}{32}\cdot t^6+\frac{3465}{64}\cdot t^4-\frac{315}{32}\cdot t^2+\frac{35}{128}$
• $P_2$:
  $\frac{6435}{128}\cdot t^{17}-\frac{517803}{2432}\cdot t^{15}+\frac{1876545}{5054}\cdot t^{13}-\frac{6070696515}{17668784}\cdot t^{11}+\frac{1702074702185}{9399793088}\cdot t^9-\frac{145391570181}{2685655168}\cdot t^7+\frac{5762999385}{671413792}\cdot t^5-\frac{820541865}{1342827584}\cdot t^3+\frac{34073955}{2685655168}\cdot t$
• $P_3$:
  $\frac{6435}{128}\cdot t^{35}-\frac{212666302487460480986604911418073705370465286570036005700874535583318870733995030645992742141739607586240501}{471570714798826798408275174025770807099023020427397976356514983940597675338338388282437104390104272148544}\cdot t^{33}+\frac{33169896486147695833449879594040686688112393855639773643464086336903696557085024512427269934725033045700769965}{17919687162355418339514456612979290669762874776241123101547569389742711662856858754732609966823962341644672}\cdot t^{31}-\frac{281702512981401093522860585626654019734412771294332472520159727614178691684510573349717959605674034983549138030}{61178931952729045424748574530249609552237314665760709338877248619668476536472244342329301214859933932021263}\cdot t^{29}+\frac{121015421343428334794178512204597011160795598109211441727154884126133231887630919852722390245994747391658989224298375}{15613673527780240252859391511589342283595378534730810682329271394755600477452199698984074030434548457197684806048}\cdot t^{27}-\frac{4080716640559250707074112907868216921129575528560753948083595903611762331752104295166491499713554113561772941194304473}{437182858777846727080062962324501583940670598972462699105219599053156813368661591571554072852167356801535174569344}\cdot t^{25}+\frac{279147732561303430954068885334206559444747507434582391979729903403023212342497847423027944328759769155581784083670536855}{33663080125894197985164848098986621963431636120879627831101909127093074629386942551009663609616886473718208441839488}\cdot t^{23}-\frac{2151887108322404084842656658788286287445126998641001235426006586612612462934794040137484240293391815032670914978373325}{389662982823732952397447422941403585686249881692847188332913120895204985828589679444211238846496991931803090377024}\cdot t^{21}+\frac{2904771220443526165697008078577376327633655257578420732932566419883293229765668514379106897488251742055657213640428325}{1047219266338782309568139949155022136531796557049526818644704012405863399414334763506317704399960665816720805388252}\cdot t^{19}-\frac{68439823846884093383659869495384833683758635186847731127502983157627809719532849930627635435227503215589216371899306725}{65258295333953592343614615778923484718613006502454723856596292141502224468766966315341061158397548859315654398931072}\cdot t^{17}+\frac{19293898994987500308620216979782479194719599742246514836991288058656697544598121062069313378914107413925187843270542385}{65258295333953592343614615778923484718613006502454723856596292141502224468766966315341061158397548859315654398931072}\cdot t^{15}-\frac{10954798720934760523623833575759702047475641710180137925779977307366938937400633798558054305680951968997221570182486185}{179460312168372378944940193392039582976185767881750490605639803389131117289109157367187918185593259363118049597060448}\cdot t^{13}+\frac{201274553707077879402265837210634911122468225581219110045563282130959245538417496657460309423522126953977996171016725}{22432539021046547368117524174004947872023220985218811325704975423641389661138644670898489773199157420389756199632556}\cdot t^{11}-\frac{11913178472964094534667833178634399420869161409358702649634300342779100186354943911445680630340072409639310358948390975}{13247433952792579245753767003121467397878440319998308942889047304724951567159694162014235415154702418441077842983007616}\cdot t^9+\frac{108857818774694281200529199740044802413365637637566450700268558246147210730045388807074706784623293399212344439150475}{1892490564684654177964823857588781056839777188571186991841292472103564509594242023144890773593528916920153977569001088}\cdot t^7-\frac{1995181442392895708620370548634833626514159796135251980212454711242394998930165515431374223826552468400326738654125}{946245282342327088982411928794390528419888594285593495920646236051782254797121011572445386796764458460076988784500544}\cdot t^5+\frac{1585249460802619459736389957905207754459393316100954479422987846492848551510296628629269512986902845802099852460875}{43527282987747046093190948724541964307314875337137300812349726858381983720667566532332487792651165089163541484087025024}\cdot t^3-\frac{90029005886785533499095121811944189271844709107565259916407229192391949238232332922721084819527483347599095862625}{478800112865217507025100435969961607380463628708510308935846995442201820927343231855657365719162815980798956324957275264}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Legendre type can be downloaded here packed into a single file.