Rule: Q[12, 78, 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.

• $P_1$:
  $4096\cdot t^{12}-11264\cdot t^{10}+11520\cdot t^8-5376\cdot t^6+1120\cdot t^4-84\cdot t^2+1$
• $P_2$:
  $4096\cdot t^{90}-91136\cdot t^{88}+979968\cdot t^{86}-6783680\cdot t^{84}+33976880\cdot t^{82}-131206068\cdot t^{80}+406481544\cdot t^{78}-1037979657\cdot t^{76}+\frac{17820735075}{8}\cdot t^{74}-\frac{130443917175}{32}\cdot t^{72}+\frac{205811513765}{32}\cdot t^{70}-\frac{9036996468045}{1024}\cdot t^{68}+\frac{43430966148115}{4096}\cdot t^{66}-\frac{183746395242025}{16384}\cdot t^{64}+\frac{21476851391925}{2048}\cdot t^{62}-\frac{142500792919755}{16384}\cdot t^{60}+\frac{1681509356453109}{262144}\cdot t^{58}-\frac{4418974509089013}{1048576}\cdot t^{56}+\frac{2589505610348965}{1048576}\cdot t^{54}-\frac{21670073265551865}{16777216}\cdot t^{52}+\frac{40471150915664469}{67108864}\cdot t^{50}-\frac{67451918192774115}{268435456}\cdot t^{48}+\frac{12530593498262385}{134217728}\cdot t^{46}-\frac{33169218083635725}{1073741824}\cdot t^{44}+\frac{78054926137112925}{8589934592}\cdot t^{42}-\frac{81460959277641489}{34359738368}\cdot t^{40}+\frac{18798682910224959}{34359738368}\cdot t^{38}-\frac{489462003181042451}{4398046511104}\cdot t^{36}+\frac{349615716557887465}{17592186044416}\cdot t^{34}-\frac{218169540588403635}{70368744177664}\cdot t^{32}+\frac{7391536347803839}{17592186044416}\cdot t^{30}-\frac{6914663035042301}{140737488355328}\cdot t^{28}+\frac{22150361247847371}{4503599627370496}\cdot t^{26}-\frac{7522327487513475}{18014398509481984}\cdot t^{24}+\frac{535645610565975}{18014398509481984}\cdot t^{22}-\frac{505037289962205}{288230376151711744}\cdot t^{20}+\frac{96926348578605}{1152921504606846976}\cdot t^{18}-\frac{14844575908435}{4611686018427387904}\cdot t^{16}+\frac{221120793075}{2305843009213693952}\cdot t^{14}-\frac{39688347475}{18446744073709551616}\cdot t^{12}+\frac{5136139085}{147573952589676412928}\cdot t^{10}-\frac{225489033}{590295810358705651712}\cdot t^8+\frac{1533939}{590295810358705651712}\cdot t^6-\frac{178365}{18889465931478580854784}\cdot t^4+\frac{1035}{75557863725914323419136}\cdot t^2-\frac{1}{302231454903657293676544}$
• $P_3$:
  $4096\cdot t^{181}-184320\cdot t^{179}+4078336\cdot t^{177}-59147264\cdot t^{175}+632385600\cdot t^{173}-5315611840\cdot t^{171}+36582584325\cdot t^{169}-211969945746\cdot t^{167}+\frac{16885720793019}{16}\cdot t^{165}-\frac{73366667414755}{16}\cdot t^{163}+\frac{4505395859893071}{256}\cdot t^{161}-\frac{1928146553542755}{32}\cdot t^{159}+\frac{94978230819806061}{512}\cdot t^{157}-\frac{264702643290702099}{512}\cdot t^{155}+\frac{21491333657649860895}{16384}\cdot t^{153}-\frac{24940242292530197853}{8192}\cdot t^{151}+\frac{3402990891119331213075}{524288}\cdot t^{149}-\frac{6688302596342557211295}{524288}\cdot t^{147}+\frac{194504539732661196299205}{8388608}\cdot t^{145}-\frac{81959452486639606448325}{2097152}\cdot t^{143}+\frac{2054652644683584998197145}{33554432}\cdot t^{141}-\frac{2999027152177903568797075}{33554432}\cdot t^{139}+\frac{522975807573423147787868115}{4294967296}\cdot t^{137}-\frac{333062798971425351708489155}{2147483648}\cdot t^{135}+\frac{12711194163276549815203731675}{68719476736}\cdot t^{133}-\frac{14213867817228223474886414859}{68719476736}\cdot t^{131}+\frac{238720087699602214770528249555}{1099511627776}\cdot t^{129}-\frac{7358396968518204469629186187}{34359738368}\cdot t^{127}+\frac{109229191363848152062157919633}{549755813888}\cdot t^{125}-\frac{95393986147151586486558922375}{549755813888}\cdot t^{123}+\frac{2511372203726590713714566998525}{17592186044416}\cdot t^{121}-\frac{973753588926246986838696667875}{8796093022208}\cdot t^{119}+\frac{91156319304682401261259857402005}{1125899906842624}\cdot t^{117}-\frac{62902865853322633207129285370145}{1125899906842624}\cdot t^{115}+\frac{655529865927710430322309166297775}{18014398509481984}\cdot t^{113}-\frac{100782142652831671600572701757345}{4503599627370496}\cdot t^{111}+\frac{936491599536586537475641315416425}{72057594037927936}\cdot t^{109}-\frac{513717572681486333604997649817435}{72057594037927936}\cdot t^{107}+\frac{17036797395770228057742348959734935}{4611686018427387904}\cdot t^{105}-\frac{4169845516447258615531344150984075}{2305843009213693952}\cdot t^{103}+\frac{61701967599711125372918734718646045}{73786976294838206464}\cdot t^{101}-\frac{26949916656161666072759004525961125}{73786976294838206464}\cdot t^{99}+\frac{177869449930666996080209429871343425}{1180591620717411303424}\cdot t^{97}-\frac{8659864468767625206515132021509275}{147573952589676412928}\cdot t^{95}+\frac{50943734984252235239907858334702125}{2361183241434822606848}\cdot t^{93}-\frac{17675368877747855827763651091310275}{2361183241434822606848}\cdot t^{91}+\frac{185116714972832403106629542759374875}{75557863725914323419136}\cdot t^{89}-\frac{28562531750733321141275070506135225}{37778931862957161709568}\cdot t^{87}+\frac{531604135718872409898059894345531725}{2417851639229258349412352}\cdot t^{85}-\frac{145605858870367845890446050545768625}{2417851639229258349412352}\cdot t^{83}+\frac{600602106346499126745682315160303795}{38685626227668133590597632}\cdot t^{81}-\frac{36408300115301922815746346002083975}{9671406556917033397649408}\cdot t^{79}+\frac{132750263497331626266644369269136955}{154742504910672534362390528}\cdot t^{77}-\frac{28406265247417898088065044937947545}{154742504910672534362390528}\cdot t^{75}+\frac{2919532817095728414606685174177942125}{79228162514264337593543950336}\cdot t^{73}-\frac{274607453232912465053198591186099925}{39614081257132168796771975168}\cdot t^{71}+\frac{1547391204725141668156912696366118625}{1267650600228229401496703205376}\cdot t^{69}-\frac{254749457283170691473411732328064161}{1267650600228229401496703205376}\cdot t^{67}+\frac{626530645220345271243285139240656129}{20282409603651670423947251286016}\cdot t^{65}-\frac{5611753057643990992257618030955305}{1267650600228229401496703205376}\cdot t^{63}+\frac{11977872919758157822818719141481651}{20282409603651670423947251286016}\cdot t^{61}-\frac{1484860279308862540018849480348965}{20282409603651670423947251286016}\cdot t^{59}+\frac{5463647178274115711768282711563611}{649037107316853453566312041152512}\cdot t^{57}-\frac{290782342821311480458255942632237}{324518553658426726783156020576256}\cdot t^{55}+\frac{7318843713383856753906950420489355}{83076749736557242056487941267521536}\cdot t^{53}-\frac{663074729588622919584732260317839}{83076749736557242056487941267521536}\cdot t^{51}+\frac{883406771395500754932637023934425}{1329227995784915872903807060280344576}\cdot t^{49}-\frac{16854094146027074753419551267795}{332306998946228968225951765070086144}\cdot t^{47}+\frac{18802142179417201040708498369955}{5316911983139663491615228241121378304}\cdot t^{45}-\frac{1193671973683662243831051262425}{5316911983139663491615228241121378304}\cdot t^{43}+\frac{4399533845862640841548731795795}{340282366920938463463374607431768211456}\cdot t^{41}-\frac{114440355082076052850842534975}{170141183460469231731687303715884105728}\cdot t^{39}+\frac{171313743668319909419140037205}{5444517870735015415413993718908291383296}\cdot t^{37}-\frac{7169470484045561120594901645}{5444517870735015415413993718908291383296}\cdot t^{35}+\frac{4270105043050159025779746225}{87112285931760246646623899502532662132736}\cdot t^{33}-\frac{17559310457402523096664377}{10889035741470030830827987437816582766592}\cdot t^{31}+\frac{8108321114887957537188615}{174224571863520493293247799005065324265472}\cdot t^{29}-\frac{203585551802381617816857}{174224571863520493293247799005065324265472}\cdot t^{27}+\frac{140943843555494966180901}{5575186299632655785383929568162090376495104}\cdot t^{25}-\frac{1299101421489753282975}{2787593149816327892691964784081045188247552}\cdot t^{23}+\frac{1288912390732970904285}{178405961588244985132285746181186892047843328}\cdot t^{21}-\frac{16542696617401533425}{178405961588244985132285746181186892047843328}\cdot t^{19}+\frac{2759805972268938747}{2854495385411919762116571938898990272765493248}\cdot t^{17}-\frac{5709711759592547}{713623846352979940529142984724747568191373312}\cdot t^{15}+\frac{582623648938015}{11417981541647679048466287755595961091061972992}\cdot t^{13}-\frac{2755891122933}{11417981541647679048466287755595961091061972992}\cdot t^{11}+\frac{1174992339235}{1461501637330902918203684832716283019655932542976}\cdot t^9-\frac{1279483491}{730750818665451459101842416358141509827966271488}\cdot t^7+\frac{51971283}{23384026197294446691258957323460528314494920687616}\cdot t^5-\frac{31395}{23384026197294446691258957323460528314494920687616}\cdot t^3+\frac{91}{374144419156711147060143317175368453031918731001856}\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.