Rule: Q[19, 38]

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.

• $P_1$:
  $262144\cdot t^{19}-1245184\cdot t^{17}+2490368\cdot t^{15}-2723840\cdot t^{13}+1770496\cdot t^{11}-695552\cdot t^9+160512\cdot t^7-20064\cdot t^5+1140\cdot t^3-19\cdot t$
• $P_2$:
  $262144\cdot t^{57}-3735552\cdot t^{55}+25214976\cdot t^{53}-107241472\cdot t^{51}+322483200\cdot t^{49}-729308160\cdot t^{47}+1288206080\cdot t^{45}-1821891456\cdot t^{43}+2098428552\cdot t^{41}-1991564135\cdot t^{39}+\frac{6279783081}{4}\cdot t^{37}-\frac{8265485241}{8}\cdot t^{35}+\frac{36429360877}{64}\cdot t^{33}-\frac{8406775587}{32}\cdot t^{31}+\frac{12987211455}{128}\cdot t^{29}-\frac{8369536271}{256}\cdot t^{27}+\frac{71651395881}{8192}\cdot t^{25}-\frac{63221819895}{32768}\cdot t^{23}+\frac{45570143685}{131072}\cdot t^{21}-\frac{13254473925}{262144}\cdot t^{19}+\frac{12251432655}{2097152}\cdot t^{17}-\frac{1101980715}{2097152}\cdot t^{15}+\frac{300540195}{8388608}\cdot t^{13}-\frac{29977155}{16777216}\cdot t^{11}+\frac{16653975}{268435456}\cdot t^9-\frac{5995431}{4294967296}\cdot t^7+\frac{312417}{17179869184}\cdot t^5-\frac{3857}{34359738368}\cdot t^3+\frac{57}{274877906944}\cdot t$

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.