Rule: Q[1, 4, 10, 76]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^5-\frac{5}{4}\cdot t^3+\frac{5}{16}\cdot t$
• $P_3$:
  $t^{15}-\frac{15}{4}\cdot t^{13}+\frac{45}{8}\cdot t^{11}-\frac{275}{64}\cdot t^9+\frac{225}{128}\cdot t^7-\frac{189}{512}\cdot t^5+\frac{35}{1024}\cdot t^3-\frac{15}{16384}\cdot t$
• $P_4$:
  $t^{91}-23\cdot t^{89}+\frac{4093}{16}\cdot t^{87}-\frac{14663}{8}\cdot t^{85}+\frac{2434145}{256}\cdot t^{83}-\frac{9742789}{256}\cdot t^{81}+\frac{125233803}{1024}\cdot t^{79}-\frac{82992897}{256}\cdot t^{77}+\frac{23685640407}{32768}\cdot t^{75}-\frac{45069663925}{32768}\cdot t^{73}+\frac{2368281785155}{1048576}\cdot t^{71}-\frac{1692675361195}{524288}\cdot t^{69}+\frac{67864001064965}{16777216}\cdot t^{67}-\frac{74930348189605}{16777216}\cdot t^{65}+\frac{73222247728025}{16777216}\cdot t^{63}-\frac{7942667146347}{2097152}\cdot t^{61}+\frac{3141949915241517}{1073741824}\cdot t^{59}-\frac{2165414329255587}{1073741824}\cdot t^{57}+\frac{21328109845237839}{17179869184}\cdot t^{55}-\frac{5868138362369745}{8589934592}\cdot t^{53}+\frac{92392123238841855}{274877906944}\cdot t^{51}-\frac{40638733321112355}{274877906944}\cdot t^{49}+\frac{63876229434821895}{1099511627776}\cdot t^{47}-\frac{5599712107651935}{274877906944}\cdot t^{45}+\frac{223933477310913825}{35184372088832}\cdot t^{43}-\frac{62203771906191531}{35184372088832}\cdot t^{41}+\frac{1961329250300137389}{4503599627370496}\cdot t^{39}-\frac{213549059302925857}{2251799813685248}\cdot t^{37}+\frac{1310495040775049143}{72057594037927936}\cdot t^{35}-\frac{220337146555501535}{72057594037927936}\cdot t^{33}+\frac{64616333879188399}{144115188075855872}\cdot t^{31}-\frac{513245006107757}{9007199254740992}\cdot t^{29}+\frac{114938592273312731}{18446744073709551616}\cdot t^{27}-\frac{10721296229571837}{18446744073709551616}\cdot t^{25}+\frac{13510911953468475}{295147905179352825856}\cdot t^{23}-\frac{443820648754665}{147573952589676412928}\cdot t^{21}+\frac{766908477350015}{4722366482869645213696}\cdot t^{19}-\frac{33429128211115}{4722366482869645213696}\cdot t^{17}+\frac{4600446448745}{18889465931478580854784}\cdot t^{15}-\frac{30349912775}{4722366482869645213696}\cdot t^{13}+\frac{75734705417}{604462909807314587353088}\cdot t^{11}-\frac{1036431451}{604462909807314587353088}\cdot t^9+\frac{296050227}{19342813113834066795298816}\cdot t^7-\frac{768867}{9671406556917033397649408}\cdot t^5+\frac{60765}{309485009821345068724781056}\cdot t^3-\frac{45}{309485009821345068724781056}\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.