Rule: Q[1, 6, 8, 16]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^7-\frac{21}{13}\cdot t^5+\frac{105}{143}\cdot t^3-\frac{35}{429}\cdot t$
• $P_3$:
  $t^{15}-\frac{825}{221}\cdot t^{13}+\frac{336705}{60401}\cdot t^{11}-\frac{8310395}{1960287}\cdot t^9+\frac{8381629155}{4854324041}\cdot t^7-\frac{250360401}{693474863}\cdot t^5+\frac{300170185}{9015173219}\cdot t^3-\frac{88221135}{99166905409}\cdot t$
• $P_4$:
  $t^{31}-\frac{22823157060610658871115730418540993373758924538995986648144983104868352501100563436229}{2864927552749720237118062263788953487770180837869410330893932022105876130184814071921}\cdot t^{29}+\frac{149363049642843434127100931142364507244522960987884793099408772303173303061407185359725416279}{5205215247402147955813879375521554868092447309803984894942912742663613694029534066921466875}\cdot t^{27}-\frac{7366631444158399017092821248931153496346880942380311314393658223822916872838498268144498602813}{119245401152024705734186336349198925055075124837988155385287639212986090352397388695485798125}\cdot t^{25}+\frac{197644159487752325277513108235696577661280979374726802652497275262292576647044180352774277774428971}{2232402694599146678026161137700261011870065818101963296020400716717449636374459705559285265561975}\cdot t^{23}-\frac{2356603366141964504071357718103715636097788476851834530765415593304963963960233115887392855498089}{26471178196827826221654084636761988283044258712671501533838743676491497664519285046157532793225}\cdot t^{21}+\frac{411653767482084348982324965244242341052345674803378424434075677846579523141243915519039612093787}{6382274041440693941160709127961161084784104481601499868559616896437298434402895291830462793755}\cdot t^{19}-\frac{465456722765954047326139736845959706965173141039726990103029508287465026791009700389391372265783}{13676301517372915588201519559916773753108795317717499718342036206651353788006204196779563129475}\cdot t^{17}+\frac{2844262635109002704577804127222640738829109832954983883065074497757518904115664377664811445525213}{217694540623594762245137128994910528093602353704373848457844411618815078531439932685208810755055}\cdot t^{15}-\frac{42599171104604213689655514039810080439709123677813128175594866074801059706027862540166435608071}{11812882049342351439658603898948633307404778883183077048100084351408570152868833556561718413065}\cdot t^{13}+\frac{27303176491737894204457256838862731200612404609034582866553617301536582976980054194297131598817}{39073379086286239377332305204214710170646576305913254851407971316197578197950757148627222443215}\cdot t^{11}-\frac{61344637727382997637100550506924811032600086767657132894122720607025040045807823554443832394859}{671351695209827203846891425781507292932018447437964106083282416251031116310244827371867731069785}\cdot t^9+\frac{70579128441925847619498653371497012727159245992528510125290236478553708927574568075366497361491}{9324329100136488942317936469187601290722478436638390362267811336819876615420067046831496264858125}\cdot t^7-\frac{10957399023242417444473062984048723359725942536272920902790451170573515423528958418280427426063}{30637081329019892239044648398759261383802429148954711190308522963836737450665934582446344870248125}\cdot t^5+\frac{2983734193807702394834605181171038664518854609074078506085209491534411511616888728417665206881}{375523082575700964872861547516220660961464060140044888589781610042456010466733883881985198552469875}\cdot t^3-\frac{579354826196938765947234421232693137268688874678414260426503268116363976609958509564329287}{10974416607903368123069783744156745310453684904114693514049869069577378464529906955900688070199625}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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