Rule: Q[5, 46]

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.

• $P_1$:
  $\frac{63}{8}\cdot t^5-\frac{35}{4}\cdot t^3+\frac{15}{8}\cdot t$
• $P_2$:
  $\frac{63}{8}\cdot t^{51}-\frac{21524040377508007313810891971332625481}{209589297859223002210312203097615048}\cdot t^{49}+\frac{13133956265194063511768917922123274642944}{20827936474760285844649775182825495395}\cdot t^{47}-\frac{4694785516351715592630619226823457987244333}{1936998092152706583552429092002771071735}\cdot t^{45}+\frac{45270343868735438376225524099922427511262937}{6923141501461560068138811162941170404196}\cdot t^{43}-\frac{11943346752089731427677872185185379654550445}{907451537010425399211125469074763131036}\cdot t^{41}+\frac{39258917811399138847010621873610989154529651993}{1914495880207744985985671958380481515703201}\cdot t^{39}-\frac{11282479418092017024047354654798304867980132}{445459509564834330584408757592368541045}\cdot t^{37}+\frac{216102995394123775881665652897339306131609067063}{8577768316180449869733375036198648626362520}\cdot t^{35}-\frac{944496568420984594940327602466095139529670850959}{46319948907374429296560225195472702582357608}\cdot t^{33}+\frac{7894250533362862239220624960501520720031451300}{584175600843323741128393644706632104726413}\cdot t^{31}-\frac{759763446658215155741279909903965923185300551646}{103286015103943787907249211827001631161466763}\cdot t^{29}+\frac{251089184208179408909747436517939301265546357953}{76319715594047133921612718098769678198128150}\cdot t^{27}-\frac{248925517851576010380927248578475564238802421713}{206345897717238547269545497081858759572716850}\cdot t^{25}+\frac{105755778492683509854556888349827469992086446498}{293011174758478737122754605856239438593257927}\cdot t^{23}-\frac{76875253746417011835357228615552968098033897180}{879033524275436211368263817568718315779773781}\cdot t^{21}+\frac{2666887395804492098101828336059577667529729462397}{157053989670544603097796468738944339085986248872}\cdot t^{19}-\frac{8862356173238723991648021168111815039957254980833}{3402836442861799733785590156010460680196368725560}\cdot t^{17}+\frac{8294919520928261856120783621974608735878549490372}{26797336987536672903561522478582377856546403713785}\cdot t^{15}-\frac{6457103554848881306113181948517161200524406381}{232357861583473638538344402443997874804453536111}\cdot t^{13}+\frac{1543248561919515435498172608170933465139793743545}{847855963236435039823454236487191014555696764535492}\cdot t^{11}-\frac{210771925672053416647609866140643093946216858889}{2543567889709305119470362709461573043667090293606476}\cdot t^9+\frac{862879492857693327087222199622759607611097863}{353273318015181266593105931869662922731540318556455}\cdot t^7-\frac{14829038823245574210541589495611718236472195144}{355746231241287535459257673392750563190661100786350185}\cdot t^5+\frac{576043164025592741500255715966813912353124917}{1707581909958180170204436832285202703315173283774480888}\cdot t^3-\frac{22822382673439416583129201343282632832434433}{27890504529316942780005801593991644154147830301649854504}\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.