Rule: Q[2, 56]

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.

• $P_1$:
  $2\cdot t^2-1$
• $P_2$:
  $2\cdot t^{58}-29\cdot t^{56}+\frac{1595}{8}\cdot t^{54}-\frac{13833}{16}\cdot t^{52}+\frac{339677}{128}\cdot t^{50}-\frac{1570205}{256}\cdot t^{48}+\frac{5676895}{512}\cdot t^{46}-\frac{16458225}{1024}\cdot t^{44}+\frac{311389617}{16384}\cdot t^{42}-\frac{607951157}{32768}\cdot t^{40}+\frac{7903365041}{524288}\cdot t^{38}-\frac{10746742019}{1048576}\cdot t^{36}+\frac{49061213565}{8388608}\cdot t^{34}-\frac{47048445829}{16777216}\cdot t^{32}+\frac{18941582087}{16777216}\cdot t^{30}-\frac{12774555361}{33554432}\cdot t^{28}+\frac{114970998249}{1073741824}\cdot t^{26}-\frac{53609145525}{2147483648}\cdot t^{24}+\frac{82200689805}{17179869184}\cdot t^{22}-\frac{25625316255}{34359738368}\cdot t^{20}+\frac{25625316255}{274877906944}\cdot t^{18}-\frac{5045911695}{549755813888}\cdot t^{16}+\frac{764532075}{1099511627776}\cdot t^{14}-\frac{86425365}{2199023255552}\cdot t^{12}+\frac{55922295}{35184372088832}\cdot t^{10}-\frac{3050307}{70368744177664}\cdot t^8+\frac{1642473}{2251799813685248}\cdot t^6-\frac{29435}{4503599627370496}\cdot t^4+\frac{841}{36028797018963968}\cdot t^2-\frac{1}{72057594037927936}$

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.