Rule: Q[2, 24, 27]

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.

• $P_1$:
  $4\cdot t^2-1$
• $P_2$:
  $4\cdot t^{26}-25\cdot t^{24}+69\cdot t^{22}-\frac{1771}{16}\cdot t^{20}+\frac{7315}{64}\cdot t^{18}-\frac{20349}{256}\cdot t^{16}+\frac{4845}{128}\cdot t^{14}-\frac{12597}{1024}\cdot t^{12}+\frac{21879}{8192}\cdot t^{10}-\frac{12155}{32768}\cdot t^8+\frac{1001}{32768}\cdot t^6-\frac{1365}{1048576}\cdot t^4+\frac{91}{4194304}\cdot t^2-\frac{1}{16777216}$
• $P_3$:
  $4\cdot t^{53}-52\cdot t^{51}+\frac{1275}{4}\cdot t^{49}-1225\cdot t^{47}+\frac{52969}{16}\cdot t^{45}-\frac{107019}{16}\cdot t^{43}+\frac{10737573}{1024}\cdot t^{41}-\frac{6690585}{512}\cdot t^{39}+\frac{215553195}{16384}\cdot t^{37}-\frac{177232627}{16384}\cdot t^{35}+\frac{1917334783}{262144}\cdot t^{33}-\frac{133767543}{32768}\cdot t^{31}+\frac{987331865}{524288}\cdot t^{29}-\frac{376038215}{524288}\cdot t^{27}+\frac{3771126099}{16777216}\cdot t^{25}-\frac{483477705}{8388608}\cdot t^{23}+\frac{6437887335}{536870912}\cdot t^{21}-\frac{1074687075}{536870912}\cdot t^{19}+\frac{2268783825}{8589934592}\cdot t^{17}-\frac{57998985}{2147483648}\cdot t^{15}+\frac{71645805}{34359738368}\cdot t^{13}-\frac{4032015}{34359738368}\cdot t^{11}+\frac{20160075}{4398046511104}\cdot t^9-\frac{254475}{2199023255552}\cdot t^7+\frac{118755}{70368744177664}\cdot t^5-\frac{819}{70368744177664}\cdot t^3+\frac{27}{1125899906842624}\cdot t$

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.