Rule: Q[1, 2, 4, 12, 54]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{4}\cdot t$
• $P_3$:
  $t^7-2\cdot t^5+\frac{19}{16}\cdot t^3-\frac{3}{16}\cdot t$
• $P_4$:
  $t^{19}-5\cdot t^{17}+\frac{169}{16}\cdot t^{15}-\frac{49}{4}\cdot t^{13}+\frac{2171}{256}\cdot t^{11}-\frac{913}{256}\cdot t^9+\frac{1815}{2048}\cdot t^7-\frac{123}{1024}\cdot t^5+\frac{489}{65536}\cdot t^3-\frac{9}{65536}\cdot t$
• $P_5$:
  $t^{73}-\frac{37}{2}\cdot t^{71}+\frac{1313}{8}\cdot t^{69}-\frac{14875}{16}\cdot t^{67}+\frac{30217}{8}\cdot t^{65}-\frac{375089}{32}\cdot t^{63}+\frac{3698331}{128}\cdot t^{61}-\frac{14868933}{256}\cdot t^{59}+\frac{6357759465}{65536}\cdot t^{57}-\frac{17889085029}{131072}\cdot t^{55}+\frac{85661767653}{524288}\cdot t^{53}-\frac{175852201551}{1048576}\cdot t^{51}+\frac{622571894295}{4194304}\cdot t^{49}-\frac{954191233275}{8388608}\cdot t^{47}+\frac{2539621368165}{33554432}\cdot t^{45}-\frac{2939489267715}{67108864}\cdot t^{43}+\frac{94762249309035}{4294967296}\cdot t^{41}-\frac{83075182012935}{8589934592}\cdot t^{39}+\frac{126615500395475}{34359738368}\cdot t^{37}-\frac{83707660854545}{68719476736}\cdot t^{35}+\frac{47872084724345}{137438953472}\cdot t^{33}-\frac{23591754285715}{274877906944}\cdot t^{31}+\frac{19938105049961}{1099511627776}\cdot t^{29}-\frac{7179915179015}{2199023255552}\cdot t^{27}+\frac{69977299992327}{140737488355328}\cdot t^{25}-\frac{17859683486619}{281474976710656}\cdot t^{23}+\frac{7553117124531}{1125899906842624}\cdot t^{21}-\frac{1304975313257}{2251799813685248}\cdot t^{19}+\frac{362118481075}{9007199254740992}\cdot t^{17}-\frac{39478084879}{18014398509481984}\cdot t^{15}+\frac{6577149193}{72057594037927936}\cdot t^{13}-\frac{403477711}{144115188075855872}\cdot t^{11}+\frac{1109136457}{18446744073709551616}\cdot t^9-\frac{31012845}{36893488147419103232}\cdot t^7+\frac{1007769}{147573952589676412928}\cdot t^5-\frac{7779}{295147905179352825856}\cdot t^3+\frac{9}{295147905179352825856}\cdot t$

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.