Rule: Q[1, 58]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{59}-\frac{59}{4}\cdot t^{57}+\frac{413}{4}\cdot t^{55}-\frac{29205}{64}\cdot t^{53}+\frac{365859}{256}\cdot t^{51}-\frac{3455335}{1024}\cdot t^{49}+\frac{3194555}{512}\cdot t^{47}-\frac{37948505}{4096}\cdot t^{45}+\frac{368323725}{32768}\cdot t^{43}-\frac{1478205883}{131072}\cdot t^{41}+\frac{1236866147}{131072}\cdot t^{39}-\frac{27773267119}{4194304}\cdot t^{37}+\frac{65592184047}{16777216}\cdot t^{35}-\frac{130526252535}{67108864}\cdot t^{33}+\frac{13674178837}{16777216}\cdot t^{31}-\frac{38536322177}{134217728}\cdot t^{29}+\frac{181927288417}{2147483648}\cdot t^{27}-\frac{178869686931}{8589934592}\cdot t^{25}+\frac{36355627425}{8589934592}\cdot t^{23}-\frac{96820776195}{137438953472}\cdot t^{21}+\frac{52134264105}{549755813888}\cdot t^{19}-\frac{22343256045}{2199023255552}\cdot t^{17}+\frac{933256395}{1099511627776}\cdot t^{15}-\frac{473390925}{8796093022208}\cdot t^{13}+\frac{175830915}{70368744177664}\cdot t^{11}-\frac{22754589}{281474976710656}\cdot t^9+\frac{477369}{281474976710656}\cdot t^7-\frac{371287}{18014398509481984}\cdot t^5+\frac{8555}{72057594037927936}\cdot t^3-\frac{59}{288230376151711744}\cdot t$

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.