Rule: Q[6, 84, 91]

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.

• $P_1$:
  $64\cdot t^6-80\cdot t^4+24\cdot t^2-1$
• $P_2$:
  $64\cdot t^{90}-1424\cdot t^{88}+15312\cdot t^{86}-105995\cdot t^{84}+\frac{2123555}{4}\cdot t^{82}-\frac{32801517}{16}\cdot t^{80}+\frac{50810193}{8}\cdot t^{78}-\frac{1037979657}{64}\cdot t^{76}+\frac{17820735075}{512}\cdot t^{74}-\frac{130443917175}{2048}\cdot t^{72}+\frac{205811513765}{2048}\cdot t^{70}-\frac{9036996468045}{65536}\cdot t^{68}+\frac{43430966148115}{262144}\cdot t^{66}-\frac{183746395242025}{1048576}\cdot t^{64}+\frac{21476851391925}{131072}\cdot t^{62}-\frac{142500792919755}{1048576}\cdot t^{60}+\frac{1681509356453109}{16777216}\cdot t^{58}-\frac{4418974509089013}{67108864}\cdot t^{56}+\frac{2589505610348965}{67108864}\cdot t^{54}-\frac{21670073265551865}{1073741824}\cdot t^{52}+\frac{40471150915664469}{4294967296}\cdot t^{50}-\frac{67451918192774115}{17179869184}\cdot t^{48}+\frac{12530593498262385}{8589934592}\cdot t^{46}-\frac{33169218083635725}{68719476736}\cdot t^{44}+\frac{78054926137112925}{549755813888}\cdot t^{42}-\frac{81460959277641489}{2199023255552}\cdot t^{40}+\frac{18798682910224959}{2199023255552}\cdot t^{38}-\frac{489462003181042451}{281474976710656}\cdot t^{36}+\frac{349615716557887465}{1125899906842624}\cdot t^{34}-\frac{218169540588403635}{4503599627370496}\cdot t^{32}+\frac{7391536347803839}{1125899906842624}\cdot t^{30}-\frac{6914663035042301}{9007199254740992}\cdot t^{28}+\frac{22150361247847371}{288230376151711744}\cdot t^{26}-\frac{7522327487513475}{1152921504606846976}\cdot t^{24}+\frac{535645610565975}{1152921504606846976}\cdot t^{22}-\frac{505037289962205}{18446744073709551616}\cdot t^{20}+\frac{96926348578605}{73786976294838206464}\cdot t^{18}-\frac{14844575908435}{295147905179352825856}\cdot t^{16}+\frac{221120793075}{147573952589676412928}\cdot t^{14}-\frac{39688347475}{1180591620717411303424}\cdot t^{12}+\frac{5136139085}{9444732965739290427392}\cdot t^{10}-\frac{225489033}{37778931862957161709568}\cdot t^8+\frac{1533939}{37778931862957161709568}\cdot t^6-\frac{178365}{1208925819614629174706176}\cdot t^4+\frac{1035}{4835703278458516698824704}\cdot t^2-\frac{1}{19342813113834066795298816}$
• $P_3$:
  $64\cdot t^{181}-2880\cdot t^{179}+63724\cdot t^{177}-924176\cdot t^{175}+9881025\cdot t^{173}-83056435\cdot t^{171}+\frac{36582584325}{64}\cdot t^{169}-\frac{105984972873}{32}\cdot t^{167}+\frac{16885720793019}{1024}\cdot t^{165}-\frac{73366667414755}{1024}\cdot t^{163}+\frac{4505395859893071}{16384}\cdot t^{161}-\frac{1928146553542755}{2048}\cdot t^{159}+\frac{94978230819806061}{32768}\cdot t^{157}-\frac{264702643290702099}{32768}\cdot t^{155}+\frac{21491333657649860895}{1048576}\cdot t^{153}-\frac{24940242292530197853}{524288}\cdot t^{151}+\frac{3402990891119331213075}{33554432}\cdot t^{149}-\frac{6688302596342557211295}{33554432}\cdot t^{147}+\frac{194504539732661196299205}{536870912}\cdot t^{145}-\frac{81959452486639606448325}{134217728}\cdot t^{143}+\frac{2054652644683584998197145}{2147483648}\cdot t^{141}-\frac{2999027152177903568797075}{2147483648}\cdot t^{139}+\frac{522975807573423147787868115}{274877906944}\cdot t^{137}-\frac{333062798971425351708489155}{137438953472}\cdot t^{135}+\frac{12711194163276549815203731675}{4398046511104}\cdot t^{133}-\frac{14213867817228223474886414859}{4398046511104}\cdot t^{131}+\frac{238720087699602214770528249555}{70368744177664}\cdot t^{129}-\frac{7358396968518204469629186187}{2199023255552}\cdot t^{127}+\frac{109229191363848152062157919633}{35184372088832}\cdot t^{125}-\frac{95393986147151586486558922375}{35184372088832}\cdot t^{123}+\frac{2511372203726590713714566998525}{1125899906842624}\cdot t^{121}-\frac{973753588926246986838696667875}{562949953421312}\cdot t^{119}+\frac{91156319304682401261259857402005}{72057594037927936}\cdot t^{117}-\frac{62902865853322633207129285370145}{72057594037927936}\cdot t^{115}+\frac{655529865927710430322309166297775}{1152921504606846976}\cdot t^{113}-\frac{100782142652831671600572701757345}{288230376151711744}\cdot t^{111}+\frac{936491599536586537475641315416425}{4611686018427387904}\cdot t^{109}-\frac{513717572681486333604997649817435}{4611686018427387904}\cdot t^{107}+\frac{17036797395770228057742348959734935}{295147905179352825856}\cdot t^{105}-\frac{4169845516447258615531344150984075}{147573952589676412928}\cdot t^{103}+\frac{61701967599711125372918734718646045}{4722366482869645213696}\cdot t^{101}-\frac{26949916656161666072759004525961125}{4722366482869645213696}\cdot t^{99}+\frac{177869449930666996080209429871343425}{75557863725914323419136}\cdot t^{97}-\frac{8659864468767625206515132021509275}{9444732965739290427392}\cdot t^{95}+\frac{50943734984252235239907858334702125}{151115727451828646838272}\cdot t^{93}-\frac{17675368877747855827763651091310275}{151115727451828646838272}\cdot t^{91}+\frac{185116714972832403106629542759374875}{4835703278458516698824704}\cdot t^{89}-\frac{28562531750733321141275070506135225}{2417851639229258349412352}\cdot t^{87}+\frac{531604135718872409898059894345531725}{154742504910672534362390528}\cdot t^{85}-\frac{145605858870367845890446050545768625}{154742504910672534362390528}\cdot t^{83}+\frac{600602106346499126745682315160303795}{2475880078570760549798248448}\cdot t^{81}-\frac{36408300115301922815746346002083975}{618970019642690137449562112}\cdot t^{79}+\frac{132750263497331626266644369269136955}{9903520314283042199192993792}\cdot t^{77}-\frac{28406265247417898088065044937947545}{9903520314283042199192993792}\cdot t^{75}+\frac{2919532817095728414606685174177942125}{5070602400912917605986812821504}\cdot t^{73}-\frac{274607453232912465053198591186099925}{2535301200456458802993406410752}\cdot t^{71}+\frac{1547391204725141668156912696366118625}{81129638414606681695789005144064}\cdot t^{69}-\frac{254749457283170691473411732328064161}{81129638414606681695789005144064}\cdot t^{67}+\frac{626530645220345271243285139240656129}{1298074214633706907132624082305024}\cdot t^{65}-\frac{5611753057643990992257618030955305}{81129638414606681695789005144064}\cdot t^{63}+\frac{11977872919758157822818719141481651}{1298074214633706907132624082305024}\cdot t^{61}-\frac{1484860279308862540018849480348965}{1298074214633706907132624082305024}\cdot t^{59}+\frac{5463647178274115711768282711563611}{41538374868278621028243970633760768}\cdot t^{57}-\frac{290782342821311480458255942632237}{20769187434139310514121985316880384}\cdot t^{55}+\frac{7318843713383856753906950420489355}{5316911983139663491615228241121378304}\cdot t^{53}-\frac{663074729588622919584732260317839}{5316911983139663491615228241121378304}\cdot t^{51}+\frac{883406771395500754932637023934425}{85070591730234615865843651857942052864}\cdot t^{49}-\frac{16854094146027074753419551267795}{21267647932558653966460912964485513216}\cdot t^{47}+\frac{18802142179417201040708498369955}{340282366920938463463374607431768211456}\cdot t^{45}-\frac{1193671973683662243831051262425}{340282366920938463463374607431768211456}\cdot t^{43}+\frac{4399533845862640841548731795795}{21778071482940061661655974875633165533184}\cdot t^{41}-\frac{114440355082076052850842534975}{10889035741470030830827987437816582766592}\cdot t^{39}+\frac{171313743668319909419140037205}{348449143727040986586495598010130648530944}\cdot t^{37}-\frac{7169470484045561120594901645}{348449143727040986586495598010130648530944}\cdot t^{35}+\frac{4270105043050159025779746225}{5575186299632655785383929568162090376495104}\cdot t^{33}-\frac{17559310457402523096664377}{696898287454081973172991196020261297061888}\cdot t^{31}+\frac{8108321114887957537188615}{11150372599265311570767859136324180752990208}\cdot t^{29}-\frac{203585551802381617816857}{11150372599265311570767859136324180752990208}\cdot t^{27}+\frac{140943843555494966180901}{356811923176489970264571492362373784095686656}\cdot t^{25}-\frac{1299101421489753282975}{178405961588244985132285746181186892047843328}\cdot t^{23}+\frac{1288912390732970904285}{11417981541647679048466287755595961091061972992}\cdot t^{21}-\frac{16542696617401533425}{11417981541647679048466287755595961091061972992}\cdot t^{19}+\frac{2759805972268938747}{182687704666362864775460604089535377456991567872}\cdot t^{17}-\frac{5709711759592547}{45671926166590716193865151022383844364247891968}\cdot t^{15}+\frac{582623648938015}{730750818665451459101842416358141509827966271488}\cdot t^{13}-\frac{2755891122933}{730750818665451459101842416358141509827966271488}\cdot t^{11}+\frac{1174992339235}{93536104789177786765035829293842113257979682750464}\cdot t^9-\frac{1279483491}{46768052394588893382517914646921056628989841375232}\cdot t^7+\frac{51971283}{1496577676626844588240573268701473812127674924007424}\cdot t^5-\frac{31395}{1496577676626844588240573268701473812127674924007424}\cdot t^3+\frac{91}{23945242826029513411849172299223580994042798784118784}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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