Rule: Q[13, 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.

• $P_1$:
  $8192\cdot t^{13}-24576\cdot t^{11}+28160\cdot t^9-15360\cdot t^7+4032\cdot t^5-448\cdot t^3+14\cdot t$
• $P_2$:
  $8192\cdot t^{69}-139264\cdot t^{67}+1132032\cdot t^{65}-5857280\cdot t^{63}+21665280\cdot t^{61}-60996096\cdot t^{59}+135891042\cdot t^{57}-245898076\cdot t^{55}+\frac{2944827765}{8}\cdot t^{53}-\frac{3695785665}{8}\cdot t^{51}+\frac{62828356305}{128}\cdot t^{49}-\frac{14230767915}{32}\cdot t^{47}+\frac{176821380645}{512}\cdot t^{45}-\frac{118119545775}{512}\cdot t^{43}+\frac{2176774486425}{16384}\cdot t^{41}-\frac{540895478445}{8192}\cdot t^{39}+\frac{14844575908435}{524288}\cdot t^{37}-\frac{5486397089355}{524288}\cdot t^{35}+\frac{27900908274925}{8388608}\cdot t^{33}-\frac{950185730725}{1048576}\cdot t^{31}+\frac{3534690918297}{16777216}\cdot t^{29}-\frac{697319977079}{16777216}\cdot t^{27}+\frac{7416948847113}{1073741824}\cdot t^{25}-\frac{514589420475}{536870912}\cdot t^{23}+\frac{1886827875075}{17179869184}\cdot t^{21}-\frac{176103935007}{17179869184}\cdot t^{19}+\frac{210585824379}{274877906944}\cdot t^{17}-\frac{3083513363}{68719476736}\cdot t^{15}+\frac{2202509545}{1099511627776}\cdot t^{13}-\frac{72243795}{1099511627776}\cdot t^{11}+\frac{52978783}{35184372088832}\cdot t^9-\frac{394383}{17592186044416}\cdot t^7+\frac{435897}{2251799813685248}\cdot t^5-\frac{1785}{2251799813685248}\cdot t^3+\frac{35}{36028797018963968}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Chebyshev U (second kind) type can be downloaded here packed into a single file.