Rule: Q[2, 4, 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.

• $P_1$:
  $2\cdot t^2-1$
• $P_2$:
  $2\cdot t^6-3\cdot t^4+\frac{9}{8}\cdot t^2-\frac{1}{16}$
• $P_3$:
  $2\cdot t^{102}-51\cdot t^{100}+\frac{5049}{8}\cdot t^{98}-\frac{80801}{16}\cdot t^{96}+\frac{469965}{16}\cdot t^{94}-\frac{4235499}{32}\cdot t^{92}+\frac{984988823}{2048}\cdot t^{90}-\frac{5932150731}{4096}\cdot t^{88}+\frac{120788686161}{32768}\cdot t^{86}-\frac{527458360715}{65536}\cdot t^{84}+\frac{7994434110663}{524288}\cdot t^{82}-\frac{26522992688823}{1048576}\cdot t^{80}+\frac{77604311941371}{2097152}\cdot t^{78}-\frac{201422427623109}{4194304}\cdot t^{76}+\frac{3727622848869225}{67108864}\cdot t^{74}-\frac{7715179551567645}{134217728}\cdot t^{72}+\frac{114651156591900585}{2147483648}\cdot t^{70}-\frac{191614216726255995}{4294967296}\cdot t^{68}+\frac{1154754459530188245}{34359738368}\cdot t^{66}-\frac{1570671094288049325}{68719476736}\cdot t^{64}+\frac{482694043610473695}{34359738368}\cdot t^{62}-\frac{536610485871490745}{68719476736}\cdot t^{60}+\frac{8634550545386714715}{2199023255552}\cdot t^{58}-\frac{7855207513221925935}{4398046511104}\cdot t^{56}+\frac{25848332415302918675}{35184372088832}\cdot t^{54}-\frac{19215046070804403441}{70368744177664}\cdot t^{52}+\frac{51577228926896030289}{562949953421312}\cdot t^{50}-\frac{31201039721208709681}{1125899906842624}\cdot t^{48}+\frac{16985894211159953919}{2251799813685248}\cdot t^{46}-\frac{8304393249197237745}{4503599627370496}\cdot t^{44}+\frac{29096133384224395951}{72057594037927936}\cdot t^{42}-\frac{11381994931311769611}{144115188075855872}\cdot t^{40}+\frac{63413971760165573547}{4611686018427387904}\cdot t^{38}-\frac{19578402348439349233}{9223372036854775808}\cdot t^{36}+\frac{21339781106430432555}{73786976294838206464}\cdot t^{34}-\frac{5105167249768645059}{147573952589676412928}\cdot t^{32}+\frac{532862574891676757}{147573952589676412928}\cdot t^{30}-\frac{96380548888931139}{295147905179352825856}\cdot t^{28}+\frac{958732828421472909}{37778931862957161709568}\cdot t^{26}-\frac{126816511695962025}{75557863725914323419136}\cdot t^{24}+\frac{56453801980783095}{604462909807314587353088}\cdot t^{22}-\frac{5214245604782445}{1208925819614629174706176}\cdot t^{20}+\frac{1572550261759785}{9671406556917033397649408}\cdot t^{18}-\frac{94836495880665}{19342813113834066795298816}\cdot t^{16}+\frac{4459396358025}{38685626227668133590597632}\cdot t^{14}-\frac{158208603735}{77371252455336267181195264}\cdot t^{12}+\frac{32427850455}{1237940039285380274899124224}\cdot t^{10}-\frac{564508035}{2475880078570760549798248448}\cdot t^8+\frac{48784645}{39614081257132168796771975168}\cdot t^6-\frac{281775}{79228162514264337593543950336}\cdot t^4+\frac{2601}{633825300114114700748351602688}\cdot t^2-\frac{1}{1267650600228229401496703205376}$

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.