Rule: Q[1, 28, 30]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{29}-\frac{29}{4}\cdot t^{27}+\frac{377}{16}\cdot t^{25}-\frac{725}{16}\cdot t^{23}+\frac{7337}{128}\cdot t^{21}-\frac{51359}{1024}\cdot t^{19}+\frac{127281}{4096}\cdot t^{17}-\frac{28101}{2048}\cdot t^{15}+\frac{140505}{32768}\cdot t^{13}-\frac{121771}{131072}\cdot t^{11}+\frac{70499}{524288}\cdot t^9-\frac{6409}{524288}\cdot t^7+\frac{2639}{4194304}\cdot t^5-\frac{1015}{67108864}\cdot t^3+\frac{29}{268435456}\cdot t$
• $P_3$:
  $t^{59}-15\cdot t^{57}+\frac{1709}{16}\cdot t^{55}-\frac{3843}{8}\cdot t^{53}+\frac{392041}{256}\cdot t^{51}-\frac{942565}{256}\cdot t^{49}+\frac{7101325}{1024}\cdot t^{47}-\frac{2686285}{256}\cdot t^{45}+\frac{425257833}{32768}\cdot t^{43}-\frac{435127363}{32768}\cdot t^{41}+\frac{11886493311}{1048576}\cdot t^{39}-\frac{4256631275}{524288}\cdot t^{37}+\frac{82123154529}{16777216}\cdot t^{35}-\frac{41738903353}{16777216}\cdot t^{33}+\frac{35755133261}{33554432}\cdot t^{31}-\frac{805055213}{2097152}\cdot t^{29}+\frac{248883578585}{2147483648}\cdot t^{27}-\frac{62630270703}{2147483648}\cdot t^{25}+\frac{208644329595}{34359738368}\cdot t^{23}-\frac{17798864985}{17179869184}\cdot t^{21}+\frac{78643211955}{549755813888}\cdot t^{19}-\frac{8648672175}{549755813888}\cdot t^{17}+\frac{2968493505}{2199023255552}\cdot t^{15}-\frac{48370695}{549755813888}\cdot t^{13}+\frac{295739535}{70368744177664}\cdot t^{11}-\frac{9852141}{70368744177664}\cdot t^9+\frac{13633335}{4503599627370496}\cdot t^7-\frac{85463}{2251799813685248}\cdot t^5+\frac{16269}{72057594037927936}\cdot t^3-\frac{29}{72057594037927936}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Chebyshev T (first kind) type can be downloaded here packed into a single file.