Rule: Q[8, 36]

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.

• $P_1$:
  $256\cdot t^8-448\cdot t^6+240\cdot t^4-40\cdot t^2+1$
• $P_2$:
  $256\cdot t^{44}-2752\cdot t^{42}+13776\cdot t^{40}-42640\cdot t^{38}+91390\cdot t^{36}-\frac{575757}{4}\cdot t^{34}+\frac{2760681}{16}\cdot t^{32}-\frac{643467}{4}\cdot t^{30}+\frac{7565085}{64}\cdot t^{28}-\frac{17651865}{256}\cdot t^{26}+\frac{32782035}{1024}\cdot t^{24}-\frac{12096045}{1024}\cdot t^{22}+\frac{28224105}{8192}\cdot t^{20}-\frac{206253075}{262144}\cdot t^{18}+\frac{145422675}{1048576}\cdot t^{16}-\frac{9694845}{524288}\cdot t^{14}+\frac{30421755}{16777216}\cdot t^{12}-\frac{8436285}{67108864}\cdot t^{10}+\frac{1562275}{268435456}\cdot t^8-\frac{44275}{268435456}\cdot t^6+\frac{5313}{2147483648}\cdot t^4-\frac{253}{17179869184}\cdot t^2+\frac{1}{68719476736}$

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.