Rule: Q[6, 7, 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.

• $P_1$:
  $64\cdot t^6-80\cdot t^4+24\cdot t^2-1$
• $P_2$:
  $64\cdot t^{13}-192\cdot t^{11}+220\cdot t^9-120\cdot t^7+\frac{63}{2}\cdot t^5-\frac{7}{2}\cdot t^3+\frac{7}{64}\cdot t$
• $P_3$:
  $64\cdot t^{55}-864\cdot t^{53}+5512\cdot t^{51}-22100\cdot t^{49}+62475\cdot t^{47}-\frac{264845}{2}\cdot t^{45}+\frac{1747977}{8}\cdot t^{43}-\frac{4601817}{16}\cdot t^{41}+\frac{314457495}{1024}\cdot t^{39}-\frac{550858165}{2048}\cdot t^{37}+\frac{1595093643}{8192}\cdot t^{35}-\frac{1917334783}{16384}\cdot t^{33}+\frac{1917334783}{32768}\cdot t^{31}-\frac{1594920705}{65536}\cdot t^{29}+\frac{2202509545}{262144}\cdot t^{27}-\frac{1257042033}{524288}\cdot t^{25}+\frac{18855630495}{33554432}\cdot t^{23}-\frac{7195285845}{67108864}\cdot t^{21}+\frac{4418157975}{268435456}\cdot t^{19}-\frac{1074687075}{536870912}\cdot t^{17}+\frac{405992895}{2147483648}\cdot t^{15}-\frac{57998985}{4294967296}\cdot t^{13}+\frac{12096045}{17179869184}\cdot t^{11}-\frac{876525}{34359738368}\cdot t^9+\frac{2629575}{4398046511104}\cdot t^7-\frac{71253}{8796093022208}\cdot t^5+\frac{1827}{35184372088832}\cdot t^3-\frac{7}{70368744177664}\cdot t$

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.