Rule: Q[9, 18, 28]

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.

• $P_1$:
  $256\cdot t^9-576\cdot t^7+432\cdot t^5-120\cdot t^3+9\cdot t$
• $P_2$:
  $256\cdot t^{27}-1728\cdot t^{25}+5184\cdot t^{23}-9108\cdot t^{21}+10395\cdot t^{19}-\frac{32319}{4}\cdot t^{17}+\frac{8721}{2}\cdot t^{15}-\frac{26163}{16}\cdot t^{13}+\frac{53703}{128}\cdot t^{11}-\frac{36465}{512}\cdot t^9+\frac{3861}{512}\cdot t^7-\frac{7371}{16384}\cdot t^5+\frac{819}{65536}\cdot t^3-\frac{27}{262144}\cdot t$
• $P_3$:
  $256\cdot t^{55}-3584\cdot t^{53}+23728\cdot t^{51}-98800\cdot t^{49}+290276\cdot t^{47}-639952\cdot t^{45}+\frac{17586789}{16}\cdot t^{43}-\frac{24118743}{16}\cdot t^{41}+\frac{429651915}{256}\cdot t^{39}-\frac{196392911}{128}\cdot t^{37}+\frac{4753056815}{4096}\cdot t^{35}-\frac{2987475127}{4096}\cdot t^{33}+\frac{3127612553}{8192}\cdot t^{31}-\frac{42605315}{256}\cdot t^{29}+\frac{15804348979}{262144}\cdot t^{27}-\frac{4738081509}{262144}\cdot t^{25}+\frac{37380460455}{8388608}\cdot t^{23}-\frac{3756287205}{4194304}\cdot t^{21}+\frac{19463777025}{134217728}\cdot t^{19}-\frac{2500779765}{134217728}\cdot t^{17}+\frac{999629565}{536870912}\cdot t^{15}-\frac{18919455}{134217728}\cdot t^{13}+\frac{536257995}{68719476736}\cdot t^{11}-\frac{20669025}{68719476736}\cdot t^9+\frac{8261955}{1099511627776}\cdot t^7-\frac{59787}{549755813888}\cdot t^5+\frac{13131}{17592186044416}\cdot t^3-\frac{27}{17592186044416}\cdot t$

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.