Rule: Q[1, 28, 30]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{29}-\frac{406}{57}\cdot t^{27}+\frac{23751}{1045}\cdot t^{25}-\frac{475020}{11077}\cdot t^{23}+\frac{910455}{17119}\cdot t^{21}-\frac{780390}{17119}\cdot t^{19}+\frac{1170585}{42347}\cdot t^{17}-\frac{208104}{17437}\cdot t^{15}+\frac{390195}{107113}\cdot t^{13}-\frac{3381690}{4391633}\cdot t^{11}+\frac{476905}{4391633}\cdot t^9-\frac{1560780}{162490421}\cdot t^7+\frac{78039}{162490421}\cdot t^5-\frac{20010}{1787394631}\cdot t^3+\frac{30015}{387864634927}\cdot t$
• $P_3$:
  $t^{59}-\frac{51271}{3477}\cdot t^{57}+\frac{147829338}{1432585}\cdot t^{55}-\frac{1497374879278}{3284188089}\cdot t^{53}+\frac{129062239636450733}{90411777149967}\cdot t^{51}-\frac{8380660773522778343}{2487210261596151}\cdot t^{49}+\frac{286966408259803665730816228}{46072304388995221528737}\cdot t^{47}-\frac{1816217692874009582848316056916}{196429759893378882256084335}\cdot t^{45}+\frac{20073610403677007096341507198448571}{1789965459510785829821967554227}\cdot t^{43}-\frac{411053438719128103440679858339889956121}{36542394618534950034768466033621539}\cdot t^{41}+\frac{97600373741932032572289204772074403484503498}{10372589907198258950862961203065697668415}\cdot t^{39}-\frac{3061149960753848401053335548288497629572958}{463757362582882083399649441083165540255}\cdot t^{37}+\frac{27014919160026088915268866807029631932833205213388403581}{6933771385386260550016988851822514001853897618402575}\cdot t^{35}-\frac{10585651097981429166855632271089488068145360552380346793}{5462889158036220151539803741181495376020311509136745}\cdot t^{33}+\frac{1924303619245004915262411666256766314540750431668170562887534088}{2370498997063731624541507692685850284866418700761737419951535}\cdot t^{31}-\frac{2365734269905430162420543099641492539625334632042572331535420958376}{8275187693468044511615306954438393285516981399578938200907845529}\cdot t^{29}+\frac{92814656365494289689533221528966172530426335285038509575946760243}{1100640727702646314352774816600180387728859595017888332140452361}\cdot t^{27}-\frac{30864357814703900601975611839093953275490503295054917057767627477}{1489471070252868943924695264629873744077516545964378797056167725}\cdot t^{25}+\frac{2759434615431199728337642249488190272024715455590750739293628506}{655367270911262335326865916437144447394107280224326670704713799}\cdot t^{23}-\frac{288568511949897217872403175763730786060905006557124843117025306}{411871130730793325363524429697652044014478488362323876055531597}\cdot t^{21}+\frac{31437540690010232381602978560442078017268390141790006317155433}{333419486782070787199043585945718321345054014388547899664001769}\cdot t^{19}-\frac{3575845056896453487167363317762592715470012005245164630388199}{354064656242260928821275386933069300994902560171120525030193829}\cdot t^{17}+\frac{210536611046723343494318949795081851416082768142433537954109684}{249615582650793954818999147787813857201406304920639970146286649445}\cdot t^{15}-\frac{127099138548945857631190379558702514213804120634383159222076}{2377291263340894807799991883693465306680060046863237810917015709}\cdot t^{13}+\frac{214645118288264453920048949906615313787388982920781645426307}{86496828273864864929953550845154545389205261705100883427980648489}\cdot t^{11}-\frac{3027520198930321945038066852128739582128111593842538479881911}{37720480475429977915362471218564214021092512763578994345820288254703}\cdot t^9+\frac{7055124680283557916754162309289887475721422186753418325382}{4191164497269997546151385690951579335676945862619888260646698694967}\cdot t^7-\frac{31905774522448489419792136792378611672984208583837962466}{1560091412464687215368222037879360517304295743631145529616980399535}\cdot t^5+\frac{4985828139369957294528073056209359138403063512940783987963}{42334952586924245213675146864301902869672830158323491320792303517861667}\cdot t^3-\frac{31508626907381284670042457929888179531604624192365687217}{155228159485388899116808871835773643855467043913852801509571779565492779}\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.