Rule: Q[1, 2, 4, 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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{5}\cdot t$
• $P_3$:
  $t^7-\frac{77}{45}\cdot t^5+\frac{749}{891}\cdot t^3-\frac{31}{297}\cdot t$
• $P_4$:
  $t^{15}-\frac{646576627207}{164781456795}\cdot t^{13}+\frac{343884350900909}{55465438357197}\cdot t^{11}-\frac{36142899049575851}{7185295423545975}\cdot t^9+\frac{1577324700316391}{714327615206325}\cdot t^7-\frac{3801532399394821}{7540124827177875}\cdot t^5+\frac{2102662882898711}{40716674066760525}\cdot t^3-\frac{233879228435939}{149294471578121925}\cdot t$
• $P_5$:
  $t^{31}-\frac{155916139588817243891959052654583117738393521847730782981572197498621478586496362545794586217855894033746656140115105462579433822004416967701956723}{18677247941136930978521670694040988861521409095164959112039873956110483344365812412562334167986843884164281057339508849125923799166359854199840255}\cdot t^{29}+\frac{90292304513854098716079175580548375919231361266147389133386089858191488657146276835496833918243274388174315734776497331531222121685257786700586066403}{2857618934993950439713815616188271295812775591560238744142100715284903951687969299122037127701987114277135001772944853916266341272453057692575559015}\cdot t^{27}-\frac{27620793788174979448892855572678355480810892161154588606061354106275081569365572102174346947619258395610096541762701583002202904503650548477356856070380571}{385221320531859489025620914140259912032041213620277983904075886923981477207296701368146214999866372940129183914001831032182284135233034442247648233017075}\cdot t^{25}+\frac{2135088493672042312739059355433458542520513393807410162361524572495654866371918365366677014969942541349959096121181823091997553355562315894623842960155742549}{19646287347124833940306666621153255513634101894634177179107870233123055337572131769775456964993185019946588379614093382641296490896884756554630059883870825}\cdot t^{23}-\frac{135126553171721132780162950722178688200894696147796948725944801845431716416006361286457846990244483437320977560830719747898036010673472383109130239113795643}{1164799645086452605156521736432011196460519875175939358445130646232592213690047338128979661956117688929639627249847433753436550843688819558574904736197875}\cdot t^{21}+\frac{772283689112101626291664975345527444055987933554530384588205990619202573436253115648102772111299097140150533530438536653887554689360445249765241486674655907}{8619517373639749278158260849596882853807847076301951252493966782121182381306350302154449498475270898079333241648871009775430476243297264733454295047864275}\cdot t^{19}-\frac{1722734140647064807658239355186402868484460131858805163487435205433741850135663414751786483890192597915123501257577889105263822472840161786275477904503793879}{34024410685420062940098398090514011265030975301191912838791974139952035715682961719030721704507648281892104901245543459639857143065647097632056427820516875}\cdot t^{17}+\frac{56665765613227314251156669284047326908092809982722784219259649182959153051421933690938506398136476583061489273979971124956559874215110686775481775680226914537}{2707942803374902656350184271556791602446288798971332827699149471256182607254061600344033321541108713258824584199130605934866277327518854299774843931832901875}\cdot t^{15}-\frac{1129122296629888099534605029770030690561849155395573867774550672131463564315975830380537043905856777985297989836778691135350076324785061787278355128482102267}{180529520224993510423345618103786106829752586598088855179943298083745507150270773356268888102740580883921638946608707062324418488501256953318322928788860125}\cdot t^{13}+\frac{14029613917698200029008810985054130580363974261030057720850399201807450013261755911581702279734918416916053477267692082488568860434976043373083478099575923}{10619383542646677083726212829634476872338387446946403245879017534337971008839457256251111064867092993171861114506394533077906969911838644312842525222874125}\cdot t^{11}-\frac{16816092000507475598130501233329041372181825175382183446324147422023376257732386674413241650025596108755177544834640516200708172868154420706315284822693203}{88623582655905905116915121614585906989151269784516347088335800877475067146496561465804726886799921524834259119244274376050169076173344322538085801405440425}\cdot t^9+\frac{498446629819059792003359336171205612244082667717346726162172139898929839318035479226413997502248862995141399350250049010090708589286421004911669545408681}{28625188196352036536471292511171158588227154323164194795974095890657321429746951377843904033204109019649308501047892240326282001347979432344342959110284375}\cdot t^7-\frac{26058335908735976303001340212800536330194408123856927215922032929661142783444318392183958654437740274727342631672404138801820811803278545788969065180999153}{28310311126192164134570108293548275843756655625609388653218380835860090894019734912687621088838863820433166107536365425682692899333151658588555186560071246875}\cdot t^5+\frac{4323021104980617385207915209872404554439860705243889139229355013820142317685034855004468686366247017917990318782711215848105716317590393816353209545444309}{186848053432868283288162714737418620568793927129021965111241313516676599900530250423738299186336501214858896309740011809505773135598800946684464231296470229375}\cdot t^3-\frac{9065800953531016069547766548808764485349323474853095849853238320490190021022665519228143109609326811980450021495639687149020343248538722101275089983679}{51450913264123150470653501159579040446479487180455323726283839953867469537827170406536633109281065551917667099783481512762459269222858231695722034704825135625}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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