Rule: Q[2, 4, 12, 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.

• $P_1$:
  $2\cdot t^2-1$
• $P_2$:
  $2\cdot t^6-3\cdot t^4+\frac{9}{8}\cdot t^2-\frac{1}{16}$
• $P_3$:
  $2\cdot t^{18}-9\cdot t^{16}+\frac{135}{8}\cdot t^{14}-\frac{273}{16}\cdot t^{12}+\frac{1287}{128}\cdot t^{10}-\frac{891}{256}\cdot t^8+\frac{693}{1024}\cdot t^6-\frac{135}{2048}\cdot t^4+\frac{81}{32768}\cdot t^2-\frac{1}{65536}$
• $P_4$:
  $2\cdot t^{90}-45\cdot t^{88}+\frac{3915}{8}\cdot t^{86}-\frac{54825}{16}\cdot t^{84}+\frac{2222325}{128}\cdot t^{82}-\frac{17365509}{256}\cdot t^{80}+\frac{108878985}{512}\cdot t^{78}-\frac{562760055}{1024}\cdot t^{76}+\frac{19559343375}{16384}\cdot t^{74}-\frac{72468842875}{32768}\cdot t^{72}+\frac{1852303623885}{524288}\cdot t^{70}-\frac{5147656215975}{1048576}\cdot t^{68}+\frac{50112653247825}{8388608}\cdot t^{66}-\frac{107384256959625}{16777216}\cdot t^{64}+\frac{50866226980875}{8388608}\cdot t^{62}-\frac{85500475751853}{16777216}\cdot t^{60}+\frac{2045078947037565}{536870912}\cdot t^{58}-\frac{2724025382315145}{1073741824}\cdot t^{56}+\frac{12947528051744825}{8589934592}\cdot t^{54}-\frac{13734553478166675}{17179869184}\cdot t^{52}+\frac{52034336891568603}{137438953472}\cdot t^{50}-\frac{43990381430070075}{274877906944}\cdot t^{48}+\frac{33169218083635725}{549755813888}\cdot t^{46}-\frac{22277833041247875}{1099511627776}\cdot t^{44}+\frac{106438535641517625}{17592186044416}\cdot t^{42}-\frac{56396048730674877}{35184372088832}\cdot t^{40}+\frac{845940730960123155}{2251799813685248}\cdot t^{38}-\frac{349615716557887465}{4503599627370496}\cdot t^{36}+\frac{507506685325965675}{36028797018963968}\cdot t^{34}-\frac{160944743057019075}{72057594037927936}\cdot t^{32}+\frac{22174609043411517}{72057594037927936}\cdot t^{30}-\frac{5273895535201755}{144115188075855872}\cdot t^{28}+\frac{34371250212176955}{9223372036854775808}\cdot t^{26}-\frac{5938679595405375}{18446744073709551616}\cdot t^{24}+\frac{3443436067924125}{147573952589676412928}\cdot t^{22}-\frac{413212328150895}{295147905179352825856}\cdot t^{20}+\frac{161543914297675}{2361183241434822606848}\cdot t^{18}-\frac{12603885205275}{4722366482869645213696}\cdot t^{16}+\frac{765418129875}{9444732965739290427392}\cdot t^{14}-\frac{35019130125}{18889465931478580854784}\cdot t^{12}+\frac{9245050353}{302231454903657293676544}\cdot t^{10}-\frac{207081765}{604462909807314587353088}\cdot t^8+\frac{23009085}{9671406556917033397649408}\cdot t^6-\frac{170775}{19342813113834066795298816}\cdot t^4+\frac{2025}{154742504910672534362390528}\cdot t^2-\frac{1}{309485009821345068724781056}$

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.