Rule: Q[1, 2, 6, 18, 54]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{4}\cdot t$
• $P_3$:
  $t^9-\frac{9}{4}\cdot t^7+\frac{27}{16}\cdot t^5-\frac{15}{32}\cdot t^3+\frac{9}{256}\cdot t$
• $P_4$:
  $t^{27}-\frac{27}{4}\cdot t^{25}+\frac{81}{4}\cdot t^{23}-\frac{2277}{64}\cdot t^{21}+\frac{10395}{256}\cdot t^{19}-\frac{32319}{1024}\cdot t^{17}+\frac{8721}{512}\cdot t^{15}-\frac{26163}{4096}\cdot t^{13}+\frac{53703}{32768}\cdot t^{11}-\frac{36465}{131072}\cdot t^9+\frac{3861}{131072}\cdot t^7-\frac{7371}{4194304}\cdot t^5+\frac{819}{16777216}\cdot t^3-\frac{27}{67108864}\cdot t$
• $P_5$:
  $t^{81}-\frac{81}{4}\cdot t^{79}+\frac{3159}{16}\cdot t^{77}-\frac{39501}{32}\cdot t^{75}+\frac{1423575}{256}\cdot t^{73}-\frac{9845145}{512}\cdot t^{71}+\frac{108734157}{2048}\cdot t^{69}-\frac{492452379}{4096}\cdot t^{67}+\frac{14915235753}{65536}\cdot t^{65}-\frac{11969016345}{32768}\cdot t^{63}+\frac{65846447667}{131072}\cdot t^{61}-\frac{156492206793}{262144}\cdot t^{59}+\frac{1293517709289}{2097152}\cdot t^{57}-\frac{2335355502291}{4194304}\cdot t^{55}+\frac{7394462517915}{16777216}\cdot t^{53}-\frac{10292494292613}{33554432}\cdot t^{51}+\frac{201891234201255}{1073741824}\cdot t^{49}-\frac{1745765378093205}{17179869184}\cdot t^{47}+\frac{3328346338128315}{68719476736}\cdot t^{45}-\frac{2797167126270825}{137438953472}\cdot t^{43}+\frac{8281448901713295}{1099511627776}\cdot t^{41}-\frac{5389514364607065}{2199023255552}\cdot t^{39}+\frac{6153513319220085}{8796093022208}\cdot t^{37}-\frac{3072143831034915}{17592186044416}\cdot t^{35}+\frac{10689623271729675}{281474976710656}\cdot t^{33}-\frac{2015757531240453}{281474976710656}\cdot t^{31}+\frac{1310947205631903}{1125899906842624}\cdot t^{29}-\frac{365051142309021}{2251799813685248}\cdot t^{27}+\frac{345371835446001}{18014398509481984}\cdot t^{25}-\frac{68707924823475}{36028797018963968}\cdot t^{23}+\frac{22723013046195}{144115188075855872}\cdot t^{21}-\frac{3078601767549}{288230376151711744}\cdot t^{19}+\frac{10743691882671}{18446744073709551616}\cdot t^{17}-\frac{1844876383893}{73786976294838206464}\cdot t^{15}+\frac{242443079235}{295147905179352825856}\cdot t^{13}-\frac{11745689553}{590295810358705651712}\cdot t^{11}+\frac{1595093643}{4722366482869645213696}\cdot t^9-\frac{35272341}{9444732965739290427392}\cdot t^7+\frac{906633}{37778931862957161709568}\cdot t^5-\frac{5535}{75557863725914323419136}\cdot t^3+\frac{81}{1208925819614629174706176}\cdot t$

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.