Rule: Q[4, 5, 8, 48]

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.

• $P_1$:
  $8\cdot t^4-8\cdot t^2+1$
• $P_2$:
  $8\cdot t^9-20\cdot t^7+17\cdot t^5-\frac{11}{2}\cdot t^3+\frac{1}{2}\cdot t$
• $P_3$:
  $8\cdot t^{17}-36\cdot t^{15}+67\cdot t^{13}-\frac{133}{2}\cdot t^{11}+\frac{605}{16}\cdot t^9-\frac{393}{32}\cdot t^7+\frac{273}{128}\cdot t^5-\frac{43}{256}\cdot t^3+\frac{1}{256}\cdot t$
• $P_4$:
  $8\cdot t^{65}-132\cdot t^{63}+1039\cdot t^{61}-\frac{10385}{2}\cdot t^{59}+\frac{296003}{16}\cdot t^{57}-\frac{1600655}{32}\cdot t^{55}+\frac{13654179}{128}\cdot t^{53}-\frac{47133801}{256}\cdot t^{51}+\frac{1072617975}{4096}\cdot t^{49}-\frac{2547050415}{8192}\cdot t^{47}+\frac{10192711165}{32768}\cdot t^{45}-\frac{17300015915}{65536}\cdot t^{43}+\frac{100092076315}{524288}\cdot t^{41}-\frac{123734259775}{1048576}\cdot t^{39}+\frac{261836368367}{4194304}\cdot t^{37}-\frac{237140973093}{8388608}\cdot t^{35}+\frac{2938136463237}{268435456}\cdot t^{33}-\frac{1940656365813}{536870912}\cdot t^{31}+\frac{2178666150595}{2147483648}\cdot t^{29}-\frac{1034046182477}{4294967296}\cdot t^{27}+\frac{1648973209611}{34359738368}\cdot t^{25}-\frac{547565693415}{68719476736}\cdot t^{23}+\frac{299711770995}{274877906944}\cdot t^{21}-\frac{66711441225}{549755813888}\cdot t^{19}+\frac{95017588965}{8796093022208}\cdot t^{17}-\frac{13247289117}{17592186044416}\cdot t^{15}+\frac{2814349167}{70368744177664}\cdot t^{13}-\frac{219631993}{140737488355328}\cdot t^{11}+\frac{47912205}{1125899906842624}\cdot t^9-\frac{1698521}{2251799813685248}\cdot t^7+\frac{69905}{9007199254740992}\cdot t^5-\frac{683}{18014398509481984}\cdot t^3+\frac{1}{18014398509481984}\cdot t$

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.