Rule: Q[1, 4, 6, 40]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^5-\frac{5}{4}\cdot t^3+\frac{5}{16}\cdot t$
• $P_3$:
  $t^{11}-3\cdot t^9+\frac{53}{16}\cdot t^7-\frac{13}{8}\cdot t^5+\frac{85}{256}\cdot t^3-\frac{5}{256}\cdot t$
• $P_4$:
  $t^{51}-13\cdot t^{49}+\frac{1273}{16}\cdot t^{47}-\frac{1219}{4}\cdot t^{45}+\frac{209715}{256}\cdot t^{43}-\frac{420497}{256}\cdot t^{41}+\frac{5220243}{2048}\cdot t^{39}-\frac{3210259}{1024}\cdot t^{37}+\frac{203461557}{65536}\cdot t^{35}-\frac{163907965}{65536}\cdot t^{33}+\frac{432375229}{262144}\cdot t^{31}-\frac{29267999}{32768}\cdot t^{29}+\frac{1666443037}{4194304}\cdot t^{27}-\frac{607545099}{4194304}\cdot t^{25}+\frac{1445389725}{33554432}\cdot t^{23}-\frac{173996955}{16777216}\cdot t^{21}+\frac{4295336595}{2147483648}\cdot t^{19}-\frac{654116895}{2147483648}\cdot t^{17}+\frac{2469143955}{68719476736}\cdot t^{15}-\frac{54977475}{17179869184}\cdot t^{13}+\frac{228524205}{1099511627776}\cdot t^{11}-\frac{10311015}{1099511627776}\cdot t^9+\frac{2408445}{8796093022208}\cdot t^7-\frac{20345}{4398046511104}\cdot t^5+\frac{10425}{281474976710656}\cdot t^3-\frac{25}{281474976710656}\cdot t$

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.