Rule: Q[10, 22, 33]

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.

• $P_1$:
  $1024\cdot t^{10}-2304\cdot t^8+1792\cdot t^6-560\cdot t^4+60\cdot t^2-1$
• $P_2$:
  $1024\cdot t^{32}-7936\cdot t^{30}+27840\cdot t^{28}-58464\cdot t^{26}+81900\cdot t^{24}-80730\cdot t^{22}+\frac{115115}{2}\cdot t^{20}-\frac{120175}{4}\cdot t^{18}+\frac{735471}{64}\cdot t^{16}-\frac{408595}{128}\cdot t^{14}+\frac{323323}{512}\cdot t^{12}-\frac{88179}{1024}\cdot t^{10}+\frac{62985}{8192}\cdot t^8-\frac{6783}{16384}\cdot t^6+\frac{765}{65536}\cdot t^4-\frac{17}{131072}\cdot t^2+\frac{1}{4194304}$
• $P_3$:
  $1024\cdot t^{65}-16384\cdot t^{63}+124992\cdot t^{61}-605120\cdot t^{59}+2087420\cdot t^{57}-5461512\cdot t^{55}+\frac{22528737}{2}\cdot t^{53}-\frac{37584261}{2}\cdot t^{51}+\frac{1652411475}{64}\cdot t^{49}-\frac{473498025}{16}\cdot t^{47}+\frac{14624324715}{512}\cdot t^{45}-\frac{11965356585}{512}\cdot t^{43}+\frac{133391567855}{8192}\cdot t^{41}-\frac{39688347475}{4096}\cdot t^{39}+\frac{323176543725}{65536}\cdot t^{37}-\frac{140676848445}{65536}\cdot t^{35}+\frac{3348108992991}{4194304}\cdot t^{33}-\frac{132638171391}{524288}\cdot t^{31}+\frac{2284324062845}{33554432}\cdot t^{29}-\frac{519280833995}{33554432}\cdot t^{27}+\frac{1584935415063}{536870912}\cdot t^{25}-\frac{125788525005}{268435456}\cdot t^{23}+\frac{263012370465}{4294967296}\cdot t^{21}-\frac{27923456925}{4294967296}\cdot t^{19}+\frac{75792240225}{137438953472}\cdot t^{17}-\frac{1257042033}{34359738368}\cdot t^{15}+\frac{2030606361}{1099511627776}\cdot t^{13}-\frac{75207643}{1099511627776}\cdot t^{11}+\frac{31100905}{17592186044416}\cdot t^9-\frac{260865}{8796093022208}\cdot t^7+\frac{40579}{140737488355328}\cdot t^5-\frac{187}{140737488355328}\cdot t^3+\frac{33}{18014398509481984}\cdot t$

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.