Rule: Q[5, 6, 10, 40]

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.

• $P_1$:
  $16\cdot t^5-20\cdot t^3+5\cdot t$
• $P_2$:
  $16\cdot t^{11}-48\cdot t^9+53\cdot t^7-26\cdot t^5+\frac{85}{16}\cdot t^3-\frac{5}{16}\cdot t$
• $P_3$:
  $16\cdot t^{21}-88\cdot t^{19}+208\cdot t^{17}-276\cdot t^{15}+\frac{3605}{16}\cdot t^{13}-\frac{3731}{32}\cdot t^{11}+\frac{2431}{64}\cdot t^9-\frac{957}{128}\cdot t^7+\frac{3333}{4096}\cdot t^5-\frac{335}{8192}\cdot t^3+\frac{5}{8192}\cdot t$
• $P_4$:
  $16\cdot t^{61}-248\cdot t^{59}+1828\cdot t^{57}-8526\cdot t^{55}+\frac{451935}{16}\cdot t^{53}-\frac{2263365}{32}\cdot t^{51}+\frac{1112735}{8}\cdot t^{49}-\frac{14100905}{64}\cdot t^{47}+\frac{585950645}{2048}\cdot t^{45}-\frac{1263121475}{4096}\cdot t^{43}+\frac{2279944667}{8192}\cdot t^{41}-\frac{3466655657}{16384}\cdot t^{39}+\frac{142632202323}{1048576}\cdot t^{37}-\frac{155385917097}{2097152}\cdot t^{35}+\frac{71742032265}{2097152}\cdot t^{33}-\frac{28043654903}{2097152}\cdot t^{31}+\frac{592414308721}{134217728}\cdot t^{29}-\frac{328847631007}{268435456}\cdot t^{27}+\frac{152595043653}{536870912}\cdot t^{25}-\frac{58733310675}{1073741824}\cdot t^{23}+\frac{297026449005}{34359738368}\cdot t^{21}-\frac{76118550255}{68719476736}\cdot t^{19}+\frac{3890274165}{34359738368}\cdot t^{17}-\frac{1242737145}{137438953472}\cdot t^{15}+\frac{2415096075}{4398046511104}\cdot t^{13}-\frac{215169357}{8796093022208}\cdot t^{11}+\frac{13379817}{17592186044416}\cdot t^9-\frac{540299}{35184372088832}\cdot t^7+\frac{809999}{4503599627370496}\cdot t^5-\frac{9005}{9007199254740992}\cdot t^3+\frac{15}{9007199254740992}\cdot t$

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.