Rule: Q[1, 18, 76, 96]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{19}-\frac{19}{4}\cdot t^{17}+\frac{19}{2}\cdot t^{15}-\frac{665}{64}\cdot t^{13}+\frac{1729}{256}\cdot t^{11}-\frac{2717}{1024}\cdot t^9+\frac{627}{1024}\cdot t^7-\frac{627}{8192}\cdot t^5+\frac{285}{65536}\cdot t^3-\frac{19}{262144}\cdot t$
• $P_3$:
  $t^{95}-\frac{95}{4}\cdot t^{93}+\frac{2185}{8}\cdot t^{91}-\frac{129675}{64}\cdot t^{89}+\frac{1395075}{128}\cdot t^{87}-\frac{23195447}{512}\cdot t^{85}+\frac{155070685}{1024}\cdot t^{83}-\frac{6853318715}{16384}\cdot t^{81}+\frac{31903380225}{32768}\cdot t^{79}-\frac{253990476675}{131072}\cdot t^{77}+\frac{874324864413}{262144}\cdot t^{75}-\frac{10503253241325}{2097152}\cdot t^{73}+\frac{27713403130725}{4194304}\cdot t^{71}-\frac{129207892645125}{16777216}\cdot t^{69}+\frac{267303100657375}{33554432}\cdot t^{67}-\frac{7880095407379415}{1073741824}\cdot t^{65}+\frac{6483622803540025}{1073741824}\cdot t^{63}-\frac{19098816493685775}{4294967296}\cdot t^{61}+\frac{25217052080407625}{8589934592}\cdot t^{59}-\frac{119519047394951375}{68719476736}\cdot t^{57}+\frac{127168266428228263}{137438953472}\cdot t^{55}-\frac{243043597999895715}{549755813888}\cdot t^{53}+\frac{208539276490570545}{1099511627776}\cdot t^{51}-\frac{1284481050847717125}{17592186044416}\cdot t^{49}+\frac{886472837908987875}{35184372088832}\cdot t^{47}-\frac{1095173871748132449}{140737488355328}\cdot t^{45}+\frac{604360163339270415}{281474976710656}\cdot t^{43}-\frac{1188969994543270555}{2251799813685248}\cdot t^{41}+\frac{519699038126589475}{4503599627370496}\cdot t^{39}-\frac{402400195665415675}{18014398509481984}\cdot t^{37}+\frac{137435143750341969}{36028797018963968}\cdot t^{35}-\frac{2637868081659789405}{4611686018427387904}\cdot t^{33}+\frac{1381740423726556355}{18446744073709551616}\cdot t^{31}-\frac{628063828966616525}{73786976294838206464}\cdot t^{29}+\frac{122947885516126475}{147573952589676412928}\cdot t^{27}-\frac{82199443459353129}{1180591620717411303424}\cdot t^{25}+\frac{11610090884089425}{2361183241434822606848}\cdot t^{23}-\frac{2737514439584925}{9444732965739290427392}\cdot t^{21}+\frac{265409987217375}{18889465931478580854784}\cdot t^{19}-\frac{166245816169125}{302231454903657293676544}\cdot t^{17}+\frac{10277014090455}{604462909807314587353088}\cdot t^{15}-\frac{974784534325}{2417851639229258349412352}\cdot t^{13}+\frac{34156870475}{4835703278458516698824704}\cdot t^{11}-\frac{3360693875}{38685626227668133590597632}\cdot t^9+\frac{53914875}{77371252455336267181195264}\cdot t^7-\frac{1006411}{309485009821345068724781056}\cdot t^5+\frac{4465}{618970019642690137449562112}\cdot t^3-\frac{95}{19807040628566084398385987584}\cdot t$
• $P_4$:
  $t^{191}-48\cdot t^{189}+\frac{18143}{16}\cdot t^{187}-\frac{281201}{16}\cdot t^{185}+\frac{25729985}{128}\cdot t^{183}-\frac{115799411}{64}\cdot t^{181}+\frac{54674446827}{4096}\cdot t^{179}-\frac{339957296367}{4096}\cdot t^{177}+\frac{14546381620947}{32768}\cdot t^{175}-\frac{16993281867925}{8192}\cdot t^{173}+\frac{4494437458989335}{524288}\cdot t^{171}-\frac{16587873596996605}{524288}\cdot t^{169}+\frac{440952187173790565}{4194304}\cdot t^{167}-\frac{664026640513473965}{2097152}\cdot t^{165}+\frac{233345063716149028475}{268435456}\cdot t^{163}-\frac{586797134151289869171}{268435456}\cdot t^{161}+\frac{10858520420523715567329}{2147483648}\cdot t^{159}-\frac{2898383872051401040593}{268435456}\cdot t^{157}+\frac{733677539082953255327043}{34359738368}\cdot t^{155}-\frac{1347485129000988628255605}{34359738368}\cdot t^{153}+\frac{18432579594824844443119125}{274877906944}\cdot t^{151}-\frac{14703962153224539477001995}{137438953472}\cdot t^{149}+\frac{1403609881657216001604752205}{8796093022208}\cdot t^{147}-\frac{1960597049448688940231163585}{8796093022208}\cdot t^{145}+\frac{20549702515455442089797102325}{70368744177664}\cdot t^{143}-\frac{6322109571627551085218898609}{17592186044416}\cdot t^{141}+\frac{468260996670317306502040463973}{1125899906842624}\cdot t^{139}-\frac{510207152086976647241108935023}{1125899906842624}\cdot t^{137}+\frac{4191205897782744538532415320663}{9007199254740992}\cdot t^{135}-\frac{2029736820818177271284346705955}{4503599627370496}\cdot t^{133}+\frac{475094568433159059368595460950871}{1152921504606846976}\cdot t^{131}-\frac{410347629422391057403449801981623}{1152921504606846976}\cdot t^{129}+\frac{1340048655159911600279216897713657}{4611686018427387904}\cdot t^{127}-\frac{32333096151645763908698309244927}{144115188075855872}\cdot t^{125}+\frac{12093763381777436680006480501935375}{73786976294838206464}\cdot t^{123}-\frac{8362626402389831600148826050217425}{73786976294838206464}\cdot t^{121}+\frac{43801814749274330543978491240757825}{590295810358705651712}\cdot t^{119}-\frac{13580443342640586587340545602774475}{295147905179352825856}\cdot t^{117}+\frac{510536283832505241151647856514640175}{18889465931478580854784}\cdot t^{115}-\frac{284121287051054179143522867261605875}{18889465931478580854784}\cdot t^{113}+\frac{1198546803204517016825139033340301815}{151115727451828646838272}\cdot t^{111}-\frac{149711984039505942743507159348443205}{37778931862957161709568}\cdot t^{109}+\frac{4536195950932833778814608028221080195}{2417851639229258349412352}\cdot t^{107}-\frac{2034752904240644252721542593605838065}{2417851639229258349412352}\cdot t^{105}+\frac{6917270938094366558131258828250940825}{19342813113834066795298816}\cdot t^{103}-\frac{1392123249481476344188196874686163225}{9671406556917033397649408}\cdot t^{101}+\frac{67921101447377406136057856212918880325}{1237940039285380274899124224}\cdot t^{99}-\frac{24510270682171615247183200663669331325}{1237940039285380274899124224}\cdot t^{97}+\frac{66968025021705289899658378085215419075}{9903520314283042199192993792}\cdot t^{95}-\frac{2704766508996727338679727963843359125}{1237940039285380274899124224}\cdot t^{93}+\frac{105786072712242188680261008144286778145}{158456325028528675187087900672}\cdot t^{91}-\frac{30552266030116576523976203320348225335}{158456325028528675187087900672}\cdot t^{89}+\frac{66686767831407657625474388893043768055}{1267650600228229401496703205376}\cdot t^{87}-\frac{8589085868495869942900161227340887505}{633825300114114700748351602688}\cdot t^{85}+\frac{133600617477179782587644350768512537275}{40564819207303340847894502572032}\cdot t^{83}-\frac{30613991271817194496274390198613702455}{40564819207303340847894502572032}\cdot t^{81}+\frac{52869855339964474866477495239416026195}{324518553658426726783156020576256}\cdot t^{79}-\frac{2685711305738118736579749220622490555}{81129638414606681695789005144064}\cdot t^{77}+\frac{32844124669969813109207521401892485915}{5192296858534827628530496329220096}\cdot t^{75}-\frac{5895808438715328653359183252278566625}{5192296858534827628530496329220096}\cdot t^{73}+\frac{7945296349748640731691893118084800025}{41538374868278621028243970633760768}\cdot t^{71}-\frac{627238838869230454039668272941426725}{20769187434139310514121985316880384}\cdot t^{69}+\frac{94930383586263396011219356110699090525}{21267647932558653966460912964485513216}\cdot t^{67}-\frac{13115827460028576450195751004618810925}{21267647932558653966460912964485513216}\cdot t^{65}+\frac{27062909110367558199137455479611095875}{340282366920938463463374607431768211456}\cdot t^{63}-\frac{203272839696848150890546248287488971}{21267647932558653966460912964485513216}\cdot t^{61}+\frac{5817692621951012921832230114191999053}{5444517870735015415413993718908291383296}\cdot t^{59}-\frac{603902529342402276482603894181319683}{5444517870735015415413993718908291383296}\cdot t^{57}+\frac{464693887096355071966452050484669363}{43556142965880123323311949751266331066368}\cdot t^{55}-\frac{20662122661158816590631481081108665}{21778071482940061661655974875633165533184}\cdot t^{53}+\frac{108460304294969188381050384156956745}{1393796574908163946345982392040522594123776}\cdot t^{51}-\frac{8183171810227644334050379635709845}{1393796574908163946345982392040522594123776}\cdot t^{49}+\frac{4530545011241272750266064401061185}{11150372599265311570767859136324180752990208}\cdot t^{47}-\frac{71672640378037494036300709271055}{2787593149816327892691964784081045188247552}\cdot t^{45}+\frac{264499488105113026032494278052925}{178405961588244985132285746181186892047843328}\cdot t^{43}-\frac{13845207004909399460606435513343}{178405961588244985132285746181186892047843328}\cdot t^{41}+\frac{5241201043975401648253920204087}{1427247692705959881058285969449495136382746624}\cdot t^{39}-\frac{111582434051881907836518464031}{713623846352979940529142984724747568191373312}\cdot t^{37}+\frac{544394051769515159108189766501}{91343852333181432387730302044767688728495783936}\cdot t^{35}-\frac{18468270742898393421114103245}{91343852333181432387730302044767688728495783936}\cdot t^{33}+\frac{4432139634280431446727682167}{730750818665451459101842416358141509827966271488}\cdot t^{31}-\frac{14588506944255723607291387}{91343852333181432387730302044767688728495783936}\cdot t^{29}+\frac{42801126889294153166744181}{11692013098647223345629478661730264157247460343808}\cdot t^{27}-\frac{845758576013757298879987}{11692013098647223345629478661730264157247460343808}\cdot t^{25}+\frac{113977324893982053542675}{93536104789177786765035829293842113257979682750464}\cdot t^{23}-\frac{807693742136374938845}{46768052394588893382517914646921056628989841375232}\cdot t^{21}+\frac{606820372311053584915}{2993155353253689176481146537402947624255349848014848}\cdot t^{19}-\frac{5789562420803022015}{2993155353253689176481146537402947624255349848014848}\cdot t^{17}+\frac{350863140092161515}{23945242826029513411849172299223580994042798784118784}\cdot t^{15}-\frac{512273187629175}{5986310706507378352962293074805895248510699696029696}\cdot t^{13}+\frac{142062562380011}{383123885216472214589586756787577295904684780545900544}\cdot t^{11}-\frac{433622387233}{383123885216472214589586756787577295904684780545900544}\cdot t^9+\frac{6925262329}{3064991081731777716716694054300618367237478244367204352}\cdot t^7-\frac{4030109}{1532495540865888858358347027150309183618739122183602176}\cdot t^5+\frac{571615}{392318858461667547739736838950479151006397215279002157056}\cdot t^3-\frac{95}{392318858461667547739736838950479151006397215279002157056}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Chebyshev T (first kind) type can be downloaded here packed into a single file.