Rule: Q[1, 2, 4, 30]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{4}\cdot t$
• $P_3$:
  $t^7-2\cdot t^5+\frac{19}{16}\cdot t^3-\frac{3}{16}\cdot t$
• $P_4$:
  $t^{37}-\frac{19}{2}\cdot t^{35}+\frac{83}{2}\cdot t^{33}-\frac{221}{2}\cdot t^{31}+\frac{51305}{256}\cdot t^{29}-\frac{134183}{512}\cdot t^{27}+\frac{261261}{1024}\cdot t^{25}-\frac{385515}{2048}\cdot t^{23}+\frac{6956235}{65536}\cdot t^{21}-\frac{6002425}{131072}\cdot t^{19}+\frac{985435}{65536}\cdot t^{17}-\frac{973199}{262144}\cdot t^{15}+\frac{5668327}{8388608}\cdot t^{13}-\frac{1476433}{16777216}\cdot t^{11}+\frac{263245}{33554432}\cdot t^9-\frac{30039}{67108864}\cdot t^7+\frac{62985}{4294967296}\cdot t^5-\frac{1947}{8589934592}\cdot t^3+\frac{9}{8589934592}\cdot t$

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.