Rule: Q[2, 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.

• $P_1$:
  $2\cdot t^2-1$
• $P_2$:
  $2\cdot t^{74}-37\cdot t^{72}+\frac{2627}{8}\cdot t^{70}-\frac{29785}{16}\cdot t^{68}+\frac{969289}{128}\cdot t^{66}-\frac{6026449}{256}\cdot t^{64}+\frac{7444437}{128}\cdot t^{62}-\frac{30015843}{256}\cdot t^{60}+\frac{804970335}{4096}\cdot t^{58}-\frac{2274557203}{8192}\cdot t^{56}+\frac{175140904631}{524288}\cdot t^{54}-\frac{361654595277}{1048576}\cdot t^{52}+\frac{2578247276007}{8388608}\cdot t^{50}-\frac{3982790558775}{16777216}\cdot t^{48}+\frac{5348318750355}{33554432}\cdot t^{46}-\frac{6254813453805}{67108864}\cdot t^{44}+\frac{102018164263785}{2147483648}\cdot t^{42}-\frac{90647718711165}{4294967296}\cdot t^{40}+\frac{280576272201225}{34359738368}\cdot t^{38}-\frac{188751310389915}{68719476736}\cdot t^{36}+\frac{440419724243135}{549755813888}\cdot t^{34}-\frac{221990534861095}{1099511627776}\cdot t^{32}+\frac{48123822242615}{1099511627776}\cdot t^{30}-\frac{17846430243425}{2199023255552}\cdot t^{28}+\frac{44973004213431}{35184372088832}\cdot t^{26}-\frac{11931613362747}{70368744177664}\cdot t^{24}+\frac{21109777487937}{1125899906842624}\cdot t^{22}-\frac{3842678171563}{2251799813685248}\cdot t^{20}+\frac{2267418796885}{18014398509481984}\cdot t^{18}-\frac{265835307221}{36028797018963968}\cdot t^{16}+\frac{24166846111}{72057594037927936}\cdot t^{14}-\frac{1649799697}{144115188075855872}\cdot t^{12}+\frac{2592542381}{9223372036854775808}\cdot t^{10}-\frac{86226465}{18446744073709551616}\cdot t^8+\frac{7101003}{147573952589676412928}\cdot t^6-\frac{78033}{295147905179352825856}\cdot t^4+\frac{1369}{2361183241434822606848}\cdot t^2-\frac{1}{4722366482869645213696}$

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.