Rule: Q[44, 90]

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.

• $P_1$:
  $17592186044416\cdot t^{44}-189115999977472\cdot t^{42}+946679511515136\cdot t^{40}-2930198488023040\cdot t^{38}+6280272978903040\cdot t^{36}-9891429941772288\cdot t^{34}+11857034609688576\cdot t^{32}-11054678884220928\cdot t^{30}+8122948166615040\cdot t^{28}-4738386430525440\cdot t^{26}+2199965128458240\cdot t^{24}-811751838842880\cdot t^{22}+236760952995840\cdot t^{20}-54068006092800\cdot t^{18}+9530420428800\cdot t^{16}-1270722723840\cdot t^{14}+124607508480\cdot t^{12}-8638755840\cdot t^{10}+399942400\cdot t^8-11334400\cdot t^6+170016\cdot t^4-1012\cdot t^2+1$
• $P_2$:
  $17592186044416\cdot t^{134}-584940185976832\cdot t^{132}+9506377533751296\cdot t^{130}-100645171238010880\cdot t^{128}+780576289907015680\cdot t^{126}-4728490986936729600\cdot t^{124}+23294232730219315200\cdot t^{122}-95945720860350873600\cdot t^{120}+337132109715996672000\cdot t^{118}-1026112413302259712000\cdot t^{116}+2737667918690428911616\cdot t^{114}-6463826636468127793152\cdot t^{112}+13610821941831260962816\cdot t^{110}-25724110195863306895360\cdot t^{108}+43870693244302888796160\cdot t^{106}-67816779973484882264064\cdot t^{104}+95385155866067497218048\cdot t^{102}-122464839946688354479104\cdot t^{100}+143922354638202125990400\cdot t^{98}-155186695008025114526400\cdot t^{96}+153837245486216200487040\cdot t^{94}-140439139519684839667680\cdot t^{92}+118237779169227823581840\cdot t^{90}-\frac{183828534772033165157325}{2}\cdot t^{88}+\frac{528300023353861078244925}{8}\cdot t^{86}-\frac{1404317516624263447989237}{32}\cdot t^{84}+\frac{1727399739926669858747523}{64}\cdot t^{82}-\frac{7869265481888162689849827}{512}\cdot t^{80}+\frac{4150013171356240670882085}{512}\cdot t^{78}-\frac{8108321114887957537188615}{2048}\cdot t^{76}+\frac{7336100056327199676503985}{4096}\cdot t^{74}-\frac{49168253727393961107288495}{65536}\cdot t^{72}+\frac{305034117784512049976284935}{1048576}\cdot t^{70}-\frac{437704928371715151926754675}{4194304}\cdot t^{68}+\frac{290358714860444704743490725}{8388608}\cdot t^{66}-\frac{711793649572175876199757263}{67108864}\cdot t^{64}+\frac{50328843909143748822205059}{16777216}\cdot t^{62}-\frac{52494122356420755114611013}{67108864}\cdot t^{60}+\frac{25207432601970899770174035}{134217728}\cdot t^{58}-\frac{356135778556050404445279315}{8589934592}\cdot t^{56}+\frac{288657420513851380445121129}{34359738368}\cdot t^{54}-\frac{214358468477073858545390937}{137438953472}\cdot t^{52}+\frac{72769925550588821410954527}{274877906944}\cdot t^{50}-\frac{90134639837685850584852675}{2199023255552}\cdot t^{48}+\frac{12696287929184520412052175}{2199023255552}\cdot t^{46}-\frac{6489213830472088210604445}{8796093022208}\cdot t^{44}+\frac{1499461720475475194731755}{17592186044416}\cdot t^{42}-\frac{2497169325588750759504915}{281474976710656}\cdot t^{40}+\frac{1865701220267457463997925}{2251799813685248}\cdot t^{38}-\frac{622490725129578831129825}{9007199254740992}\cdot t^{36}+\frac{92275095725090509085127}{18014398509481984}\cdot t^{34}-\frac{48334573951237885711257}{144115188075855872}\cdot t^{32}+\frac{1388667092204239533873}{72057594037927936}\cdot t^{30}-\frac{277989040547098111935}{288230376151711744}\cdot t^{28}+\frac{24023744244810947945}{576460752303423488}\cdot t^{26}-\frac{28391697743867483935}{18446744073709551616}\cdot t^{24}+\frac{3542544564786358755}{73786976294838206464}\cdot t^{22}-\frac{368118665976450235}{295147905179352825856}\cdot t^{20}+\frac{15661116555200525}{590295810358705651712}\cdot t^{18}-\frac{2137511893796325}{4722366482869645213696}\cdot t^{16}+\frac{28500158583951}{4722366482869645213696}\cdot t^{14}-\frac{1149098108613}{18889465931478580854784}\cdot t^{12}+\frac{16756622883}{37778931862957161709568}\cdot t^{10}-\frac{1329890705}{604462909807314587353088}\cdot t^8+\frac{131115985}{19342813113834066795298816}\cdot t^6-\frac{864501}{77371252455336267181195264}\cdot t^4+\frac{1139}{154742504910672534362390528}\cdot t^2-\frac{1}{1237940039285380274899124224}$

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.