Rule: Q[1, 4, 72]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^5-2\cdot t^3+\frac{3}{8}\cdot t$
• $P_3$:
  $2\cdot t^{77}-38\cdot t^{75}+\frac{2775}{8}\cdot t^{73}-\frac{8103}{4}\cdot t^{71}+\frac{544215}{64}\cdot t^{69}-\frac{1748943}{64}\cdot t^{67}+\frac{143218999}{2048}\cdot t^{65}-\frac{18730855}{128}\cdot t^{63}+\frac{1045181709}{4096}\cdot t^{61}-\frac{1540002035}{4096}\cdot t^{59}+\frac{30999335081}{65536}\cdot t^{57}-\frac{16782543687}{32768}\cdot t^{55}+\frac{251738155305}{524288}\cdot t^{53}-\frac{205263418941}{524288}\cdot t^{51}+\frac{37387265592825}{134217728}\cdot t^{49}-\frac{5815796869995}{33554432}\cdot t^{47}+\frac{202802465047245}{2147483648}\cdot t^{45}-\frac{96805419670575}{2147483648}\cdot t^{43}+\frac{647520696018735}{34359738368}\cdot t^{41}-\frac{118413686604675}{17179869184}\cdot t^{39}+\frac{605134770855615}{274877906944}\cdot t^{37}-\frac{168345763320735}{274877906944}\cdot t^{35}+\frac{1300853625660225}{8796093022208}\cdot t^{33}-\frac{33935311973745}{1099511627776}\cdot t^{31}+\frac{194813827997425}{35184372088832}\cdot t^{29}-\frac{29846948742247}{35184372088832}\cdot t^{27}+\frac{61989816618513}{562949953421312}\cdot t^{25}-\frac{3376351667675}{281474976710656}\cdot t^{23}+\frac{4881239839553}{4503599627370496}\cdot t^{21}-\frac{360682746765}{4503599627370496}\cdot t^{19}+\frac{1370594437707}{288230376151711744}\cdot t^{17}-\frac{15991836267}{72057594037927936}\cdot t^{15}+\frac{73006209045}{9223372036854775808}\cdot t^{13}-\frac{1917334783}{9223372036854775808}\cdot t^{11}+\frac{563921995}{147573952589676412928}\cdot t^9-\frac{3372291}{73786976294838206464}\cdot t^7+\frac{374699}{1180591620717411303424}\cdot t^5-\frac{1235}{1180591620717411303424}\cdot t^3+\frac{39}{37778931862957161709568}\cdot t$

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.