Rule: Q[1, 6, 42]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^7-\frac{7}{4}\cdot t^5+\frac{7}{8}\cdot t^3-\frac{7}{64}\cdot t$
• $P_3$:
  $t^{49}-\frac{49}{4}\cdot t^{47}+\frac{1127}{16}\cdot t^{45}-\frac{8085}{32}\cdot t^{43}+\frac{162239}{256}\cdot t^{41}-\frac{604709}{512}\cdot t^{39}+\frac{3473561}{2048}\cdot t^{37}-\frac{7868679}{4096}\cdot t^{35}+\frac{114191805}{65536}\cdot t^{33}-\frac{83740657}{65536}\cdot t^{31}+\frac{199689259}{262144}\cdot t^{29}-\frac{193956553}{524288}\cdot t^{27}+\frac{613322073}{4194304}\cdot t^{25}-\frac{393155175}{8388608}\cdot t^{23}+\frac{405992895}{33554432}\cdot t^{21}-\frac{167173545}{67108864}\cdot t^{19}+\frac{866262915}{2147483648}\cdot t^{17}-\frac{866262915}{17179869184}\cdot t^{15}+\frac{326012925}{68719476736}\cdot t^{13}-\frac{44612295}{137438953472}\cdot t^{11}+\frac{16921905}{1099511627776}\cdot t^9-\frac{1036035}{2199023255552}\cdot t^7+\frac{73255}{8796093022208}\cdot t^5-\frac{1225}{17592186044416}\cdot t^3+\frac{49}{281474976710656}\cdot t$

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.