Rule: Q[30, 32]

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.

• $P_1$:
  $\frac{7391536347803839}{67108864}\cdot t^{30}-\frac{54496920530418135}{67108864}\cdot t^{28}+\frac{180700315442965395}{67108864}\cdot t^{26}-\frac{355924863751295475}{67108864}\cdot t^{24}+\frac{463373879223384675}{67108864}\cdot t^{22}-\frac{419762220002360235}{67108864}\cdot t^{20}+\frac{271274904083157975}{67108864}\cdot t^{18}-\frac{126155198555389575}{67108864}\cdot t^{16}+\frac{42051732851796525}{67108864}\cdot t^{14}-\frac{9888133564634325}{67108864}\cdot t^{12}+\frac{1591748329916745}{67108864}\cdot t^{10}-\frac{166966608033225}{67108864}\cdot t^8+\frac{10529425731825}{67108864}\cdot t^6-\frac{347123925225}{67108864}\cdot t^4+\frac{4508102925}{67108864}\cdot t^2-\frac{9694845}{67108864}$
• $P_2$:
  $\frac{7391536347803839}{67108864}\cdot t^{62}-\frac{1014215431703863807}{603979776}\cdot t^{60}+\frac{30102688622807786158877}{2473297182720}\cdot t^{58}-\frac{582582527912478931894605113}{10439787408261120}\cdot t^{56}+\frac{178642174672327350198623068490237}{983271377047073587200}\cdot t^{54}-\frac{1965745486886597486165216118200452381}{4398172869531560155545600}\cdot t^{52}+\frac{76037585863691175375069293933854077716162717}{88089443052478934651567603712000}\cdot t^{50}-\frac{104925071461404497532222865640266980976566853}{78163872004312294127447310336000}\cdot t^{48}+\frac{894195427499707921176638058003530029435009383308411}{522692364215556892989947369603727360000}\cdot t^{46}-\frac{63059058097357603979368075152232499236911025041492369637}{34859294615791077195906971984137864347648000}\cdot t^{44}+\frac{81133568422029970212425339039794374925158408156314929229548013}{50675828065340883696619862847640816848784588800000}\cdot t^{42}-\frac{316172182479208779707251872049497534771680244765192266139567113689}{264983904953667480849625262830313831302294614835200000}\cdot t^{40}+\frac{91748131482672813964102532722538654534865900579536641305120124528016363647}{122067176949707190705573183761981172212101570096756948992000000}\cdot t^{38}-\frac{89429068780155120404514959550329930415872140099294023444724535824880516086661}{223016732287115037419082206733139601631509568566774945808384000000}\cdot t^{36}+\frac{14732179277003821828770790651240304075808721388879102166316860558520673695939619687}{81279563165700510962571605654926393512611819812003962874594590720000000}\cdot t^{34}-\frac{21377245576010556837719121536498839762408493581839392296634435329309551923711177227843}{308338652717619643428911988232032225293520872041509868833545917562880000000}\cdot t^{32}+\frac{51349279398001286411178059555424284778915671683383767981590225980949845618437809335258267367}{2294229204490511483191813973319082456002350803325138952690914257407128371200000000}\cdot t^{30}-\frac{32027486456138265130660263524700398394136420599100889916077007143958560774548972234837973}{5274090125265543639521411432917430933338737478908365408484860361855467520000000}\cdot t^{28}+\frac{115239613487175397508698758486678003560335559559871383501681460637677641856647746706527}{83715716274056248246371610046308427513313293316005800134680323204055040000000}\cdot t^{26}-\frac{999496760274285306753476984922124331028505692492084883756722098972449538354903971309}{3863802289571826842140228155983465885229844306892575390831399532494848000000}\cdot t^{24}+\frac{28279076268208573344609155765032758860665834404161292520234324028674003288758923}{708824489006022168802096524671338448950622694348298549042634293248000000}\cdot t^{22}-\frac{28487844494873313536271463301294223304965147616443309919642057703195414235181361}{5713993329742423605649553617248544639499917638113835242282460119040000000}\cdot t^{20}+\frac{83439000676833494657359155508962206201976517161516817563276272717231807805429179}{167991403894427254006096876347107212401297578560546756123104327499776000000}\cdot t^{18}-\frac{35334869881575096721038140617469582699647629859602151342245018962603426186754803}{914619865647437271810971882334250378629286816607421227781345783054336000000}\cdot t^{16}+\frac{6265481476672591319333501683490006932190572769019150202311742421135257882177777}{2743859596942311815432915647002751135887860449822263683344037349163008000000}\cdot t^{14}-\frac{26844855274471002130488017800107430233254012308649134392927980260683562971587}{271370729367920948779079569483788573879019165367037067583476221345792000000}\cdot t^{12}+\frac{103977980257762186645285412663221425867885966661242996708446318368564606517}{34791119149733454971676867882536996651156303252184239433779002736640000000}\cdot t^{10}-\frac{22964204788039529528639188789298253299065369344763315630718287049503388611}{391979942420330259347559378143250162269694349974609097620576764166144000000}\cdot t^8+\frac{111810705134413572746975513290449771307067473703069135174657419763531683}{167991403894427254006096876347107212401297578560546756123104327499776000000}\cdot t^6-\frac{18270910636376893056608832852649572217111087326254867057003349924964819}{5095739251464293371518271915862252109506026549669918269067497934159872000000}\cdot t^4+\frac{41287225976728666721564970403633510127310065395284517898513171480461}{7134034952050010720125580682207152953308437169537885576694497107823820800000}\cdot t^2-\frac{7630469509596484263397146536523834185222776327971376307958337583}{535052621403750804009418551165536471498132787715341418252087283086786560000000}$

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.