Rule: Q[18, 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.

• $P_1$:
  $262144\cdot t^{18}-1114112\cdot t^{16}+1966080\cdot t^{14}-1863680\cdot t^{12}+1025024\cdot t^{10}-329472\cdot t^8+59136\cdot t^6-5280\cdot t^4+180\cdot t^2-1$
• $P_2$:
  $262144\cdot t^{56}-3604480\cdot t^{54}+23445504\cdot t^{52}-95952896\cdot t^{50}+277222400\cdot t^{48}-601359360\cdot t^{46}+1017004800\cdot t^{44}-1374409344\cdot t^{42}+1509395976\cdot t^{40}-1362649145\cdot t^{38}+\frac{4076350421}{4}\cdot t^{36}-\frac{5075297955}{8}\cdot t^{34}+\frac{21090682613}{64}\cdot t^{32}-\frac{4572106021}{32}\cdot t^{30}+\frac{6607528635}{128}\cdot t^{28}-\frac{3964517181}{256}\cdot t^{26}+\frac{31426050825}{8192}\cdot t^{24}-\frac{25510558905}{32768}\cdot t^{22}+\frac{16789000305}{131072}\cdot t^{20}-\frac{4418157975}{262144}\cdot t^{18}+\frac{3653936055}{2097152}\cdot t^{16}-\frac{289994925}{2097152}\cdot t^{14}+\frac{68544255}{8388608}\cdot t^{12}-\frac{5785065}{16777216}\cdot t^{10}+\frac{2629575}{268435456}\cdot t^8-\frac{736281}{4294967296}\cdot t^6+\frac{27405}{17179869184}\cdot t^4-\frac{203}{34359738368}\cdot t^2+\frac{1}{274877906944}$

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.