Rule: Q[6, 14, 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.

• $P_1$:
  $64\cdot t^6-80\cdot t^4+24\cdot t^2-1$
• $P_2$:
  $64\cdot t^{20}-304\cdot t^{18}+612\cdot t^{16}-680\cdot t^{14}+455\cdot t^{12}-\frac{3003}{16}\cdot t^{10}+\frac{3003}{64}\cdot t^8-\frac{429}{64}\cdot t^6+\frac{495}{1024}\cdot t^4-\frac{55}{4096}\cdot t^2+\frac{1}{16384}$
• $P_3$:
  $64\cdot t^{62}-976\cdot t^{60}+7080\cdot t^{58}-32509\cdot t^{56}+\frac{212135}{2}\cdot t^{54}-\frac{2093553}{8}\cdot t^{52}+\frac{8117109}{16}\cdot t^{50}-\frac{202927725}{256}\cdot t^{48}+\frac{520232895}{512}\cdot t^{46}-\frac{2215806775}{2048}\cdot t^{44}+\frac{3955006055}{4096}\cdot t^{42}-\frac{23813008485}{32768}\cdot t^{40}+\frac{30349912775}{65536}\cdot t^{38}-\frac{65649195941}{262144}\cdot t^{36}+\frac{60290077905}{524288}\cdot t^{34}-\frac{751616304549}{16777216}\cdot t^{32}+\frac{495746924277}{33554432}\cdot t^{30}-\frac{551534301945}{134217728}\cdot t^{28}+\frac{257382674241}{268435456}\cdot t^{26}-\frac{400236215925}{2147483648}\cdot t^{24}+\frac{128447901855}{4294967296}\cdot t^{22}-\frac{67282234305}{17179869184}\cdot t^{20}+\frac{14172532725}{34359738368}\cdot t^{18}-\frac{18855630495}{549755813888}\cdot t^{16}+\frac{2417388525}{1099511627776}\cdot t^{14}-\frac{463120749}{4398046511104}\cdot t^{12}+\frac{31773357}{8796093022208}\cdot t^{10}-\frac{5883955}{70368744177664}\cdot t^8+\frac{168113}{140737488355328}\cdot t^6-\frac{5115}{562949953421312}\cdot t^4+\frac{31}{1125899906842624}\cdot t^2-\frac{1}{72057594037927936}$

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.