Rule: Q[1, 2, 16, 36]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{4}\cdot t$
• $P_3$:
  $t^{19}-5\cdot t^{17}+\frac{169}{16}\cdot t^{15}-\frac{49}{4}\cdot t^{13}+\frac{2171}{256}\cdot t^{11}-\frac{913}{256}\cdot t^9+\frac{1815}{2048}\cdot t^7-\frac{123}{1024}\cdot t^5+\frac{489}{65536}\cdot t^3-\frac{9}{65536}\cdot t$
• $P_4$:
  $t^{55}-14\cdot t^{53}+\frac{1483}{16}\cdot t^{51}-\frac{6175}{16}\cdot t^{49}+\frac{72569}{64}\cdot t^{47}-\frac{39997}{16}\cdot t^{45}+\frac{17586789}{4096}\cdot t^{43}-\frac{24118743}{4096}\cdot t^{41}+\frac{429651915}{65536}\cdot t^{39}-\frac{196392911}{32768}\cdot t^{37}+\frac{4753056815}{1048576}\cdot t^{35}-\frac{2987475127}{1048576}\cdot t^{33}+\frac{3127612553}{2097152}\cdot t^{31}-\frac{42605315}{65536}\cdot t^{29}+\frac{15804348979}{67108864}\cdot t^{27}-\frac{4738081509}{67108864}\cdot t^{25}+\frac{37380460455}{2147483648}\cdot t^{23}-\frac{3756287205}{1073741824}\cdot t^{21}+\frac{19463777025}{34359738368}\cdot t^{19}-\frac{2500779765}{34359738368}\cdot t^{17}+\frac{999629565}{137438953472}\cdot t^{15}-\frac{18919455}{34359738368}\cdot t^{13}+\frac{536257995}{17592186044416}\cdot t^{11}-\frac{20669025}{17592186044416}\cdot t^9+\frac{8261955}{281474976710656}\cdot t^7-\frac{59787}{140737488355328}\cdot t^5+\frac{13131}{4503599627370496}\cdot t^3-\frac{27}{4503599627370496}\cdot t$

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.