Rule: Q[1, 4, 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.

• $P_1$:
  $t$
• $P_2$:
  $t^5-\frac{5}{4}\cdot t^3+\frac{5}{16}\cdot t$
• $P_3$:
  $t^{11}-3\cdot t^9+\frac{53}{16}\cdot t^7-\frac{13}{8}\cdot t^5+\frac{85}{256}\cdot t^3-\frac{5}{256}\cdot t$
• $P_4$:
  $t^{21}-\frac{11}{2}\cdot t^{19}+13\cdot t^{17}-\frac{69}{4}\cdot t^{15}+\frac{3605}{256}\cdot t^{13}-\frac{3731}{512}\cdot t^{11}+\frac{2431}{1024}\cdot t^9-\frac{957}{2048}\cdot t^7+\frac{3333}{65536}\cdot t^5-\frac{335}{131072}\cdot t^3+\frac{5}{131072}\cdot t$
• $P_5$:
  $t^{61}-\frac{31}{2}\cdot t^{59}+\frac{457}{4}\cdot t^{57}-\frac{4263}{8}\cdot t^{55}+\frac{451935}{256}\cdot t^{53}-\frac{2263365}{512}\cdot t^{51}+\frac{1112735}{128}\cdot t^{49}-\frac{14100905}{1024}\cdot t^{47}+\frac{585950645}{32768}\cdot t^{45}-\frac{1263121475}{65536}\cdot t^{43}+\frac{2279944667}{131072}\cdot t^{41}-\frac{3466655657}{262144}\cdot t^{39}+\frac{142632202323}{16777216}\cdot t^{37}-\frac{155385917097}{33554432}\cdot t^{35}+\frac{71742032265}{33554432}\cdot t^{33}-\frac{28043654903}{33554432}\cdot t^{31}+\frac{592414308721}{2147483648}\cdot t^{29}-\frac{328847631007}{4294967296}\cdot t^{27}+\frac{152595043653}{8589934592}\cdot t^{25}-\frac{58733310675}{17179869184}\cdot t^{23}+\frac{297026449005}{549755813888}\cdot t^{21}-\frac{76118550255}{1099511627776}\cdot t^{19}+\frac{3890274165}{549755813888}\cdot t^{17}-\frac{1242737145}{2199023255552}\cdot t^{15}+\frac{2415096075}{70368744177664}\cdot t^{13}-\frac{215169357}{140737488355328}\cdot t^{11}+\frac{13379817}{281474976710656}\cdot t^9-\frac{540299}{562949953421312}\cdot t^7+\frac{809999}{72057594037927936}\cdot t^5-\frac{9005}{144115188075855872}\cdot t^3+\frac{15}{144115188075855872}\cdot t$

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.