Rule: Q[1, 18, 20]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{19}-\frac{19}{4}\cdot t^{17}+\frac{19}{2}\cdot t^{15}-\frac{665}{64}\cdot t^{13}+\frac{1729}{256}\cdot t^{11}-\frac{2717}{1024}\cdot t^9+\frac{627}{1024}\cdot t^7-\frac{627}{8192}\cdot t^5+\frac{285}{65536}\cdot t^3-\frac{19}{262144}\cdot t$
• $P_3$:
  $t^{39}-10\cdot t^{37}+\frac{739}{16}\cdot t^{35}-\frac{2091}{16}\cdot t^{33}+\frac{8107}{32}\cdot t^{31}-\frac{713}{2}\cdot t^{29}+\frac{1541785}{4096}\cdot t^{27}-\frac{1245231}{4096}\cdot t^{25}+\frac{12435345}{65536}\cdot t^{23}-\frac{3009435}{32768}\cdot t^{21}+\frac{36063885}{1048576}\cdot t^{19}-\frac{10367825}{1048576}\cdot t^{17}+\frac{9026235}{4194304}\cdot t^{15}-\frac{364021}{1048576}\cdot t^{13}+\frac{5400883}{134217728}\cdot t^{11}-\frac{429913}{134217728}\cdot t^9+\frac{702525}{4294967296}\cdot t^7-\frac{10317}{2147483648}\cdot t^5+\frac{4579}{68719476736}\cdot t^3-\frac{19}{68719476736}\cdot t$

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.