Rule: Q[2, 20, 44]

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.

• $P_1$:
  $2\cdot t^2-1$
• $P_2$:
  $2\cdot t^{22}-11\cdot t^{20}+\frac{209}{8}\cdot t^{18}-\frac{561}{16}\cdot t^{16}+\frac{935}{32}\cdot t^{14}-\frac{1001}{64}\cdot t^{12}+\frac{11011}{2048}\cdot t^{10}-\frac{4719}{4096}\cdot t^8+\frac{4719}{32768}\cdot t^6-\frac{605}{65536}\cdot t^4+\frac{121}{524288}\cdot t^2-\frac{1}{1048576}$
• $P_3$:
  $2\cdot t^{66}-33\cdot t^{64}+\frac{2079}{8}\cdot t^{62}-\frac{20801}{16}\cdot t^{60}+\frac{593835}{128}\cdot t^{58}-\frac{3218391}{256}\cdot t^{56}+\frac{27535123}{1024}\cdot t^{54}-\frac{95406201}{2048}\cdot t^{52}+\frac{2181183147}{32768}\cdot t^{50}-\frac{5208478275}{65536}\cdot t^{48}+\frac{20982726765}{262144}\cdot t^{46}-\frac{35896069755}{524288}\cdot t^{44}+\frac{209615320915}{4194304}\cdot t^{42}-\frac{261943093335}{8388608}\cdot t^{40}+\frac{561306628575}{33554432}\cdot t^{38}-\frac{515815110965}{67108864}\cdot t^{36}+\frac{6499270398159}{2147483648}\cdot t^{34}-\frac{4377059655903}{4294967296}\cdot t^{32}+\frac{5025512938259}{17179869184}\cdot t^{30}-\frac{2448038217405}{34359738368}\cdot t^{28}+\frac{4023297592083}{274877906944}\cdot t^{26}-\frac{1383673775055}{549755813888}\cdot t^{24}+\frac{789037111395}{2199023255552}\cdot t^{22}-\frac{184294815705}{4398046511104}\cdot t^{20}+\frac{277904880825}{70368744177664}\cdot t^{18}-\frac{41482387089}{140737488355328}\cdot t^{16}+\frac{9572858559}{562949953421312}\cdot t^{14}-\frac{827284073}{1125899906842624}\cdot t^{12}+\frac{205265973}{9007199254740992}\cdot t^{10}-\frac{8608545}{18014398509481984}\cdot t^8+\frac{446369}{72057594037927936}\cdot t^6-\frac{6171}{144115188075855872}\cdot t^4+\frac{1089}{9223372036854775808}\cdot t^2-\frac{1}{18446744073709551616}$

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.