Rule: Q[8, 36, 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.

• $P_1$:
  $256\cdot t^8-448\cdot t^6+240\cdot t^4-40\cdot t^2+1$
• $P_2$:
  $256\cdot t^{44}-2752\cdot t^{42}+13776\cdot t^{40}-42640\cdot t^{38}+91390\cdot t^{36}-\frac{575757}{4}\cdot t^{34}+\frac{2760681}{16}\cdot t^{32}-\frac{643467}{4}\cdot t^{30}+\frac{7565085}{64}\cdot t^{28}-\frac{17651865}{256}\cdot t^{26}+\frac{32782035}{1024}\cdot t^{24}-\frac{12096045}{1024}\cdot t^{22}+\frac{28224105}{8192}\cdot t^{20}-\frac{206253075}{262144}\cdot t^{18}+\frac{145422675}{1048576}\cdot t^{16}-\frac{9694845}{524288}\cdot t^{14}+\frac{30421755}{16777216}\cdot t^{12}-\frac{8436285}{67108864}\cdot t^{10}+\frac{1562275}{268435456}\cdot t^8-\frac{44275}{268435456}\cdot t^6+\frac{5313}{2147483648}\cdot t^4-\frac{253}{17179869184}\cdot t^2+\frac{1}{68719476736}$
• $P_3$:
  $256\cdot t^{134}-8512\cdot t^{132}+138336\cdot t^{130}-1464580\cdot t^{128}+11358880\cdot t^{126}-68808600\cdot t^{124}+338975700\cdot t^{122}-\frac{89356415775}{64}\cdot t^{120}+\frac{1255914977625}{256}\cdot t^{118}-\frac{15290266473625}{1024}\cdot t^{116}+\frac{81588861903263}{2048}\cdot t^{114}-\frac{1541096362225563}{16384}\cdot t^{112}+\frac{3245072827775779}{16384}\cdot t^{110}-\frac{24532423206198985}{65536}\cdot t^{108}+\frac{83676706780057695}{131072}\cdot t^{106}-\frac{2069603881026760323}{2097152}\cdot t^{104}+\frac{23287391568864135063}{16777216}\cdot t^{102}-\frac{119594570260437846171}{67108864}\cdot t^{100}+\frac{281098348902738527325}{134217728}\cdot t^{98}-\frac{2424792109500392414475}{1073741824}\cdot t^{96}+\frac{1201853480361064066305}{536870912}\cdot t^{94}-\frac{4388723109990151239615}{2147483648}\cdot t^{92}+\frac{7389861198076738973865}{4294967296}\cdot t^{90}-\frac{183828534772033165157325}{137438953472}\cdot t^{88}+\frac{528300023353861078244925}{549755813888}\cdot t^{86}-\frac{1404317516624263447989237}{2199023255552}\cdot t^{84}+\frac{1727399739926669858747523}{4398046511104}\cdot t^{82}-\frac{7869265481888162689849827}{35184372088832}\cdot t^{80}+\frac{4150013171356240670882085}{35184372088832}\cdot t^{78}-\frac{8108321114887957537188615}{140737488355328}\cdot t^{76}+\frac{7336100056327199676503985}{281474976710656}\cdot t^{74}-\frac{49168253727393961107288495}{4503599627370496}\cdot t^{72}+\frac{305034117784512049976284935}{72057594037927936}\cdot t^{70}-\frac{437704928371715151926754675}{288230376151711744}\cdot t^{68}+\frac{290358714860444704743490725}{576460752303423488}\cdot t^{66}-\frac{711793649572175876199757263}{4611686018427387904}\cdot t^{64}+\frac{50328843909143748822205059}{1152921504606846976}\cdot t^{62}-\frac{52494122356420755114611013}{4611686018427387904}\cdot t^{60}+\frac{25207432601970899770174035}{9223372036854775808}\cdot t^{58}-\frac{356135778556050404445279315}{590295810358705651712}\cdot t^{56}+\frac{288657420513851380445121129}{2361183241434822606848}\cdot t^{54}-\frac{214358468477073858545390937}{9444732965739290427392}\cdot t^{52}+\frac{72769925550588821410954527}{18889465931478580854784}\cdot t^{50}-\frac{90134639837685850584852675}{151115727451828646838272}\cdot t^{48}+\frac{12696287929184520412052175}{151115727451828646838272}\cdot t^{46}-\frac{6489213830472088210604445}{604462909807314587353088}\cdot t^{44}+\frac{1499461720475475194731755}{1208925819614629174706176}\cdot t^{42}-\frac{2497169325588750759504915}{19342813113834066795298816}\cdot t^{40}+\frac{1865701220267457463997925}{154742504910672534362390528}\cdot t^{38}-\frac{622490725129578831129825}{618970019642690137449562112}\cdot t^{36}+\frac{92275095725090509085127}{1237940039285380274899124224}\cdot t^{34}-\frac{48334573951237885711257}{9903520314283042199192993792}\cdot t^{32}+\frac{1388667092204239533873}{4951760157141521099596496896}\cdot t^{30}-\frac{277989040547098111935}{19807040628566084398385987584}\cdot t^{28}+\frac{24023744244810947945}{39614081257132168796771975168}\cdot t^{26}-\frac{28391697743867483935}{1267650600228229401496703205376}\cdot t^{24}+\frac{3542544564786358755}{5070602400912917605986812821504}\cdot t^{22}-\frac{368118665976450235}{20282409603651670423947251286016}\cdot t^{20}+\frac{15661116555200525}{40564819207303340847894502572032}\cdot t^{18}-\frac{2137511893796325}{324518553658426726783156020576256}\cdot t^{16}+\frac{28500158583951}{324518553658426726783156020576256}\cdot t^{14}-\frac{1149098108613}{1298074214633706907132624082305024}\cdot t^{12}+\frac{16756622883}{2596148429267413814265248164610048}\cdot t^{10}-\frac{1329890705}{41538374868278621028243970633760768}\cdot t^8+\frac{131115985}{1329227995784915872903807060280344576}\cdot t^6-\frac{864501}{5316911983139663491615228241121378304}\cdot t^4+\frac{1139}{10633823966279326983230456482242756608}\cdot t^2-\frac{1}{85070591730234615865843651857942052864}$

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.