Rule: Q[1, 2, 64]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^3-1\cdot t$
• $P_3$:
  $2\cdot t^{67}-33\cdot t^{65}+260\cdot t^{63}-1302\cdot t^{61}+\frac{595665}{128}\cdot t^{59}-\frac{3235501}{256}\cdot t^{57}+\frac{13881343}{512}\cdot t^{55}-\frac{48275865}{1024}\cdot t^{53}+\frac{2217471399}{32768}\cdot t^{51}-\frac{5324436975}{65536}\cdot t^{49}+\frac{5397877485}{65536}\cdot t^{47}-\frac{9306388455}{131072}\cdot t^{45}+\frac{219364870725}{4194304}\cdot t^{43}-\frac{277044025545}{8388608}\cdot t^{41}+\frac{300497488025}{16777216}\cdot t^{39}-\frac{280086337895}{33554432}\cdot t^{37}+\frac{7174519270695}{2147483648}\cdot t^{35}-\frac{4923689695575}{4294967296}\cdot t^{33}+\frac{722141155351}{2147483648}\cdot t^{31}-\frac{360682746765}{4294967296}\cdot t^{29}+\frac{4881239839553}{274877906944}\cdot t^{27}-\frac{1735881645069}{549755813888}\cdot t^{25}+\frac{514589420475}{1099511627776}\cdot t^{23}-\frac{125788525005}{2199023255552}\cdot t^{21}+\frac{400236215925}{70368744177664}\cdot t^{19}-\frac{63665481789}{140737488355328}\cdot t^{17}+\frac{3964517181}{140737488355328}\cdot t^{15}-\frac{376038215}{281474976710656}\cdot t^{13}+\frac{419014011}{9007199254740992}\cdot t^{11}-\frac{20376455}{18014398509481984}\cdot t^9+\frac{643467}{36028797018963968}\cdot t^7-\frac{11781}{72057594037927936}\cdot t^5+\frac{6545}{9223372036854775808}\cdot t^3-\frac{17}{18446744073709551616}\cdot t$

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.