Rule: Q[3, 8, 12, 24]

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.

• $P_1$:
  $8\cdot t^3-4\cdot t$
• $P_2$:
  $8\cdot t^{11}-20\cdot t^9+18\cdot t^7-7\cdot t^5+\frac{35}{32}\cdot t^3-\frac{3}{64}\cdot t$
• $P_3$:
  $8\cdot t^{23}-44\cdot t^{21}+105\cdot t^{19}-\frac{285}{2}\cdot t^{17}+\frac{969}{8}\cdot t^{15}-\frac{1071}{16}\cdot t^{13}+\frac{1547}{64}\cdot t^{11}-\frac{715}{128}\cdot t^9+\frac{6435}{8192}\cdot t^7-\frac{1001}{16384}\cdot t^5+\frac{143}{65536}\cdot t^3-\frac{3}{131072}\cdot t$
• $P_4$:
  $8\cdot t^{47}-92\cdot t^{45}+495\cdot t^{43}-\frac{3311}{2}\cdot t^{41}+\frac{61705}{16}\cdot t^{39}-\frac{212667}{32}\cdot t^{37}+\frac{1124097}{128}\cdot t^{35}-\frac{2330445}{256}\cdot t^{33}+\frac{15380937}{2048}\cdot t^{31}-\frac{20376455}{4096}\cdot t^{29}+\frac{43541267}{16384}\cdot t^{27}-\frac{37550331}{32768}\cdot t^{25}+\frac{104306475}{262144}\cdot t^{23}-\frac{57998985}{524288}\cdot t^{21}+\frac{51175575}{2097152}\cdot t^{19}-\frac{17678835}{4194304}\cdot t^{17}+\frac{300540195}{536870912}\cdot t^{15}-\frac{59879925}{1073741824}\cdot t^{13}+\frac{17298645}{4294967296}\cdot t^{11}-\frac{1726725}{8589934592}\cdot t^9+\frac{444015}{68719476736}\cdot t^7-\frac{16445}{137438953472}\cdot t^5+\frac{575}{549755813888}\cdot t^3-\frac{3}{1099511627776}\cdot t$

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.