Rule: Q[2, 18, 42]

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.

• $P_1$:
  $4\cdot t^2-1$
• $P_2$:
  $4\cdot t^{20}-19\cdot t^{18}+\frac{153}{4}\cdot t^{16}-\frac{85}{2}\cdot t^{14}+\frac{455}{16}\cdot t^{12}-\frac{3003}{256}\cdot t^{10}+\frac{3003}{1024}\cdot t^8-\frac{429}{1024}\cdot t^6+\frac{495}{16384}\cdot t^4-\frac{55}{65536}\cdot t^2+\frac{1}{262144}$
• $P_3$:
  $4\cdot t^{62}-61\cdot t^{60}+\frac{885}{2}\cdot t^{58}-\frac{32509}{16}\cdot t^{56}+\frac{212135}{32}\cdot t^{54}-\frac{2093553}{128}\cdot t^{52}+\frac{8117109}{256}\cdot t^{50}-\frac{202927725}{4096}\cdot t^{48}+\frac{520232895}{8192}\cdot t^{46}-\frac{2215806775}{32768}\cdot t^{44}+\frac{3955006055}{65536}\cdot t^{42}-\frac{23813008485}{524288}\cdot t^{40}+\frac{30349912775}{1048576}\cdot t^{38}-\frac{65649195941}{4194304}\cdot t^{36}+\frac{60290077905}{8388608}\cdot t^{34}-\frac{751616304549}{268435456}\cdot t^{32}+\frac{495746924277}{536870912}\cdot t^{30}-\frac{551534301945}{2147483648}\cdot t^{28}+\frac{257382674241}{4294967296}\cdot t^{26}-\frac{400236215925}{34359738368}\cdot t^{24}+\frac{128447901855}{68719476736}\cdot t^{22}-\frac{67282234305}{274877906944}\cdot t^{20}+\frac{14172532725}{549755813888}\cdot t^{18}-\frac{18855630495}{8796093022208}\cdot t^{16}+\frac{2417388525}{17592186044416}\cdot t^{14}-\frac{463120749}{70368744177664}\cdot t^{12}+\frac{31773357}{140737488355328}\cdot t^{10}-\frac{5883955}{1125899906842624}\cdot t^8+\frac{168113}{2251799813685248}\cdot t^6-\frac{5115}{9007199254740992}\cdot t^4+\frac{31}{18014398509481984}\cdot t^2-\frac{1}{1152921504606846976}$

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.