Rule: Q[6, 84]

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.

• $P_1$:
  $64\cdot t^6-80\cdot t^4+24\cdot t^2-1$
• $P_2$:
  $64\cdot t^{90}-1424\cdot t^{88}+15312\cdot t^{86}-105995\cdot t^{84}+\frac{2123555}{4}\cdot t^{82}-\frac{32801517}{16}\cdot t^{80}+\frac{50810193}{8}\cdot t^{78}-\frac{1037979657}{64}\cdot t^{76}+\frac{17820735075}{512}\cdot t^{74}-\frac{130443917175}{2048}\cdot t^{72}+\frac{205811513765}{2048}\cdot t^{70}-\frac{9036996468045}{65536}\cdot t^{68}+\frac{43430966148115}{262144}\cdot t^{66}-\frac{183746395242025}{1048576}\cdot t^{64}+\frac{21476851391925}{131072}\cdot t^{62}-\frac{142500792919755}{1048576}\cdot t^{60}+\frac{1681509356453109}{16777216}\cdot t^{58}-\frac{4418974509089013}{67108864}\cdot t^{56}+\frac{2589505610348965}{67108864}\cdot t^{54}-\frac{21670073265551865}{1073741824}\cdot t^{52}+\frac{40471150915664469}{4294967296}\cdot t^{50}-\frac{67451918192774115}{17179869184}\cdot t^{48}+\frac{12530593498262385}{8589934592}\cdot t^{46}-\frac{33169218083635725}{68719476736}\cdot t^{44}+\frac{78054926137112925}{549755813888}\cdot t^{42}-\frac{81460959277641489}{2199023255552}\cdot t^{40}+\frac{18798682910224959}{2199023255552}\cdot t^{38}-\frac{489462003181042451}{281474976710656}\cdot t^{36}+\frac{349615716557887465}{1125899906842624}\cdot t^{34}-\frac{218169540588403635}{4503599627370496}\cdot t^{32}+\frac{7391536347803839}{1125899906842624}\cdot t^{30}-\frac{6914663035042301}{9007199254740992}\cdot t^{28}+\frac{22150361247847371}{288230376151711744}\cdot t^{26}-\frac{7522327487513475}{1152921504606846976}\cdot t^{24}+\frac{535645610565975}{1152921504606846976}\cdot t^{22}-\frac{505037289962205}{18446744073709551616}\cdot t^{20}+\frac{96926348578605}{73786976294838206464}\cdot t^{18}-\frac{14844575908435}{295147905179352825856}\cdot t^{16}+\frac{221120793075}{147573952589676412928}\cdot t^{14}-\frac{39688347475}{1180591620717411303424}\cdot t^{12}+\frac{5136139085}{9444732965739290427392}\cdot t^{10}-\frac{225489033}{37778931862957161709568}\cdot t^8+\frac{1533939}{37778931862957161709568}\cdot t^6-\frac{178365}{1208925819614629174706176}\cdot t^4+\frac{1035}{4835703278458516698824704}\cdot t^2-\frac{1}{19342813113834066795298816}$

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.