Rule: Q[1, 2, 4, 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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{4}\cdot t$
• $P_3$:
  $t^7-2\cdot t^5+\frac{19}{16}\cdot t^3-\frac{3}{16}\cdot t$
• $P_4$:
  $t^{49}-\frac{25}{2}\cdot t^{47}+\frac{587}{8}\cdot t^{45}-\frac{4301}{16}\cdot t^{43}+\frac{88193}{128}\cdot t^{41}-\frac{336077}{256}\cdot t^{39}+\frac{1974765}{1024}\cdot t^{37}-\frac{4578639}{2048}\cdot t^{35}+\frac{34024497}{16384}\cdot t^{33}-\frac{51138329}{32768}\cdot t^{31}+\frac{125047087}{131072}\cdot t^{29}-\frac{124632865}{262144}\cdot t^{27}+\frac{404709123}{2097152}\cdot t^{25}-\frac{266611935}{4194304}\cdot t^{23}+\frac{283171515}{16777216}\cdot t^{21}-\frac{120029985}{33554432}\cdot t^{19}+\frac{2563431075}{4294967296}\cdot t^{17}-\frac{660960315}{8589934592}\cdot t^{15}+\frac{256818345}{34359738368}\cdot t^{13}-\frac{36324015}{68719476736}\cdot t^{11}+\frac{14257815}{549755813888}\cdot t^9-\frac{904475}{1099511627776}\cdot t^7+\frac{66355}{4398046511104}\cdot t^5-\frac{1153}{8796093022208}\cdot t^3+\frac{3}{8796093022208}\cdot t$

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.