Rule: Q[4, 60]

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.

• $P_1$:
  $16\cdot t^4-12\cdot t^2+1$
• $P_2$:
  $16\cdot t^{64}-252\cdot t^{62}+1891\cdot t^{60}-\frac{17995}{2}\cdot t^{58}+\frac{487635}{16}\cdot t^{56}-\frac{2503193}{32}\cdot t^{54}+\frac{20237679}{128}\cdot t^{52}-\frac{66096459}{256}\cdot t^{50}+\frac{1420494075}{4096}\cdot t^{48}-\frac{3179201025}{8192}\cdot t^{46}+\frac{11965356585}{32768}\cdot t^{44}-\frac{19055938265}{65536}\cdot t^{42}+\frac{103189703435}{524288}\cdot t^{40}-\frac{119065042425}{1048576}\cdot t^{38}+\frac{234461414075}{4194304}\cdot t^{36}-\frac{196947587823}{8388608}\cdot t^{34}+\frac{2254848913647}{268435456}\cdot t^{32}-\frac{1370594437707}{536870912}\cdot t^{30}+\frac{1409476549415}{2147483648}\cdot t^{28}-\frac{609590544255}{4294967296}\cdot t^{26}+\frac{880519675035}{34359738368}\cdot t^{24}-\frac{263012370465}{68719476736}\cdot t^{22}+\frac{128447901855}{274877906944}\cdot t^{20}-\frac{25264080075}{549755813888}\cdot t^{18}+\frac{31426050825}{8796093022208}\cdot t^{16}-\frac{3771126099}{17592186044416}\cdot t^{14}+\frac{676868787}{70368744177664}\cdot t^{12}-\frac{43541267}{140737488355328}\cdot t^{10}+\frac{7565085}{1125899906842624}\cdot t^8-\frac{202895}{2251799813685248}\cdot t^6+\frac{5797}{9007199254740992}\cdot t^4-\frac{33}{18014398509481984}\cdot t^2+\frac{1}{1152921504606846976}$

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.