Rule: Q[2, 4, 6, 29]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^6-\frac{25}{14}\cdot t^4+\frac{45}{98}\cdot t^2-\frac{1}{98}$
• $P_3$:
  $\frac{3}{2}\cdot t^{12}-\frac{1595}{364}\cdot t^{10}+\frac{318813}{66248}\cdot t^8-\frac{10310751}{4183088}\cdot t^6+\frac{2471775}{4183088}\cdot t^4-\frac{33827}{597584}\cdot t^2+\frac{31245}{29281616}$
• $P_4$:
  $\frac{3}{2}\cdot t^{41}-\frac{200878654664870721002356981670774076294062513277236691787769718660280181776686150147511416482124742715746383335039744459}{13098896957413181817464871223832828865583339979972714427224843514161912270225101895778436692789697406609026877724435820}\cdot t^{39}+\frac{2295302302975720884225651232683393379303410141210102984129085542936241618827088569792657772341529950532286020195007285589685563}{31594188410842135870452561333335984503973418398182723929719672930352352856534103739886782440905383380850475707151016182960024}\cdot t^{37}-\frac{14776021912362221081063870549817506301993151090670429892735738907373725397122950835413073895082091615464125766820377812195109881427}{69823156387961120273700160546672525753781254659983819884680477176078699812940369265149789194400897271679551312803745764341653040}\cdot t^{35}+\frac{35551421321614917583385162262057209079390946084386077382347846196329495777619545373612089410279599953788081275077301648669908793}{83821316192030156390996591292524040520745803913546002262521581243791956558151703799699626884034690602256364121012900077240880}\cdot t^{33}-\frac{2219486859970114367437194513661428323725230974062928460313806836273463245491065557557473267456055017098277022524077074602156670397}{3579170201399687677895554448190776530235845827108414296609671519109916545033077752247174067948281288716346747967250833298185576}\cdot t^{31}+\frac{5057192984323960857602962985343288659888489067636335439194814104001132813685905130208909954610044330394985527937543456214614030304181}{7390986465890355054854319935513953534937021632978875522498971686961977665493305558390414450313200861199256034552372970760753214440}\cdot t^{29}-\frac{122790717808097070962475171046624280030327441233311728102911758959025475600158721945973653070353835958243030088417244900618940746913}{211171041882581572995837712443255815283914903799396443499970619627485076156951587382583270008948596034264458130067799164592948984}\cdot t^{27}+\frac{6253760023184224830464403033974554949945314612629956463201325302008729494289647621011937528683941474990308074351397382998864222293}{16243926298660120999679824034096601175685761830722803346151586125191159704380891337121790000688353541097266010005215320353303768}\cdot t^{25}-\frac{1202994473361673679769802528231559763575613761601924736277490683069995958861306183893540915403437666204153178796931817878535221630377}{6026496656802904890881214716649839036179417639198160041422238452445920250325310686072184090255379163747085689711934883851075697928}\cdot t^{23}+\frac{361014699688345899241077046278861031544366710182037906980379941749505305334833857533175997900610393330271459331798227857512571643425}{4454367094158668832390463051436837548480439124624726987138176247460028011110012246227266501493106338421758988047951870672534211512}\cdot t^{21}-\frac{14277052664657074335063685526487999126647667038908176107728506812917929598569742088227598637966709179082724294709718760120891512128}{556795886769833604048807881429604693560054890578090873392272030932503501388751530778408312686638292302719873505993983834066776439}\cdot t^{19}+\frac{13940926389762880860449577034111517217954999352486534511651394818309763025799547738286244549093218208495180279058087748632730042575}{2227183547079334416195231525718418774240219562312363493569088123730014005555006123113633250746553169210879494023975935336267105756}\cdot t^{17}-\frac{2129347366776518885319525939721855642072168583853239261788032811250023209837268816080458362172795132986127894472180075029807108403}{1834151156418275401572543609415168402315474933669005229998072572483540945751181513152403853555984962879547818607980182041631734152}\cdot t^{15}+\frac{84714269755935830610783758720633677314948821290562739337775784646808072852191958342971339018615288443487625231067105193185405276633}{529545641017333512368301519232579334439939262992151367118014952712748035909019691154429741148092229997080877343818278272305390674456}\cdot t^{13}-\frac{8402617301659407497753974641976470890898897368504232110045145726918406536122470655708304721018257940988725511024444663909893156755}{529545641017333512368301519232579334439939262992151367118014952712748035909019691154429741148092229997080877343818278272305390674456}\cdot t^{11}+\frac{52182695521120303529417194088202094239780456917500216826561072225074469573694784644001896942281057497223116534406672053054585785453}{48188653332577349625515438250164719434034472932285774407739360696860071267720791895053106444476392929734359838287463322779790551375496}\cdot t^9-\frac{2292387538373890546262498328937135861526864145876677713076169144123855829494642001142675857660726325857845560379096611122852651185}{48188653332577349625515438250164719434034472932285774407739360696860071267720791895053106444476392929734359838287463322779790551375496}\cdot t^7+\frac{2083995789649506032397264057916930218226218966072953845396206159562919856155861571386384450790558137422083876991056017186479083}{1721023333306333915196979937505882836929802604724491943133548596316431116704313996251896658731299747490512851367409404384992519691982}\cdot t^5-\frac{203609874592532875451378189184252401014214549605873128554173998378707760397699603882150892520806429544751748481692156833063113}{13768186666450671321575839500047062695438420837795935545068388770531448933634511970015173269850397979924102810939275235079940157535856}\cdot t^3+\frac{91374323838570304703853779495263468018464413181294175237794053309382828436189406729724568302318755831710206533275762711359705}{1638414213307629887267524900505600460757172079697716329863138263693242423102506924431805619112197359610968234501773752974512878746766864}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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