Rule: Q[4, 10, 30]

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.

• $P_1$:
  $16\cdot t^4-12\cdot t^2+1$
• $P_2$:
  $16\cdot t^{14}-52\cdot t^{12}+66\cdot t^{10}-\frac{165}{4}\cdot t^8+\frac{105}{8}\cdot t^6-\frac{63}{32}\cdot t^4+\frac{7}{64}\cdot t^2-\frac{1}{1024}$
• $P_3$:
  $16\cdot t^{44}-172\cdot t^{42}+861\cdot t^{40}-2665\cdot t^{38}+\frac{45695}{8}\cdot t^{36}-\frac{575757}{64}\cdot t^{34}+\frac{2760681}{256}\cdot t^{32}-\frac{643467}{64}\cdot t^{30}+\frac{7565085}{1024}\cdot t^{28}-\frac{17651865}{4096}\cdot t^{26}+\frac{32782035}{16384}\cdot t^{24}-\frac{12096045}{16384}\cdot t^{22}+\frac{28224105}{131072}\cdot t^{20}-\frac{206253075}{4194304}\cdot t^{18}+\frac{145422675}{16777216}\cdot t^{16}-\frac{9694845}{8388608}\cdot t^{14}+\frac{30421755}{268435456}\cdot t^{12}-\frac{8436285}{1073741824}\cdot t^{10}+\frac{1562275}{4294967296}\cdot t^8-\frac{44275}{4294967296}\cdot t^6+\frac{5313}{34359738368}\cdot t^4-\frac{253}{274877906944}\cdot t^2+\frac{1}{1099511627776}$

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.