Rule: Q[2, 3, 8, 12, 24]

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.

• $P_1$:
  $2\cdot t^2-1$
• $P_2$:
  $2\cdot t^5-3\cdot t^3+1\cdot t$
• $P_3$:
  $2\cdot t^{13}-7\cdot t^{11}+\frac{19}{2}\cdot t^9-\frac{25}{4}\cdot t^7+\frac{259}{128}\cdot t^5-\frac{73}{256}\cdot t^3+\frac{3}{256}\cdot t$
• $P_4$:
  $2\cdot t^{25}-13\cdot t^{23}+\frac{149}{4}\cdot t^{21}-\frac{495}{8}\cdot t^{19}+\frac{2109}{32}\cdot t^{17}-\frac{3009}{64}\cdot t^{15}+\frac{5831}{256}\cdot t^{13}-\frac{3809}{512}\cdot t^{11}+\frac{52195}{32768}\cdot t^9-\frac{13871}{65536}\cdot t^7+\frac{4147}{262144}\cdot t^5-\frac{289}{524288}\cdot t^3+\frac{3}{524288}\cdot t$
• $P_5$:
  $2\cdot t^{49}-25\cdot t^{47}+\frac{587}{4}\cdot t^{45}-\frac{4301}{8}\cdot t^{43}+\frac{88193}{64}\cdot t^{41}-\frac{336077}{128}\cdot t^{39}+\frac{1974765}{512}\cdot t^{37}-\frac{4578639}{1024}\cdot t^{35}+\frac{34024497}{8192}\cdot t^{33}-\frac{51138329}{16384}\cdot t^{31}+\frac{125047087}{65536}\cdot t^{29}-\frac{124632865}{131072}\cdot t^{27}+\frac{404709123}{1048576}\cdot t^{25}-\frac{266611935}{2097152}\cdot t^{23}+\frac{283171515}{8388608}\cdot t^{21}-\frac{120029985}{16777216}\cdot t^{19}+\frac{2563431075}{2147483648}\cdot t^{17}-\frac{660960315}{4294967296}\cdot t^{15}+\frac{256818345}{17179869184}\cdot t^{13}-\frac{36324015}{34359738368}\cdot t^{11}+\frac{14257815}{274877906944}\cdot t^9-\frac{904475}{549755813888}\cdot t^7+\frac{66355}{2199023255552}\cdot t^5-\frac{1153}{4398046511104}\cdot t^3+\frac{3}{4398046511104}\cdot t$

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.