Rule: Q[2, 24, 27]

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.

• $P_1$:
  $2\cdot t^2-1$
• $P_2$:
  $2\cdot t^{26}-13\cdot t^{24}+\frac{299}{8}\cdot t^{22}-\frac{1001}{16}\cdot t^{20}+\frac{8645}{128}\cdot t^{18}-\frac{12597}{256}\cdot t^{16}+\frac{12597}{512}\cdot t^{14}-\frac{8619}{1024}\cdot t^{12}+\frac{31603}{16384}\cdot t^{10}-\frac{9295}{32768}\cdot t^8+\frac{13013}{524288}\cdot t^6-\frac{1183}{1048576}\cdot t^4+\frac{169}{8388608}\cdot t^2-\frac{1}{16777216}$
• $P_3$:
  $2\cdot t^{53}-27\cdot t^{51}+172\cdot t^{49}-\frac{1375}{2}\cdot t^{47}+\frac{247549}{128}\cdot t^{45}-\frac{1042107}{256}\cdot t^{43}+\frac{3407019}{512}\cdot t^{41}-\frac{8862601}{1024}\cdot t^{39}+\frac{298290785}{32768}\cdot t^{37}-\frac{512962931}{65536}\cdot t^{35}+\frac{363083331}{65536}\cdot t^{33}-\frac{212381221}{65536}\cdot t^{31}+\frac{3289500799}{2097152}\cdot t^{29}-\frac{2632267505}{4194304}\cdot t^{27}+\frac{1735430499}{8388608}\cdot t^{25}-\frac{937382805}{16777216}\cdot t^{23}+\frac{13165769595}{1073741824}\cdot t^{21}-\frac{4643330505}{2147483648}\cdot t^{19}+\frac{324111975}{1073741824}\cdot t^{17}-\frac{140500215}{4294967296}\cdot t^{15}+\frac{1474166715}{549755813888}\cdot t^{13}-\frac{176498205}{1099511627776}\cdot t^{11}+\frac{14697345}{2199023255552}\cdot t^9-\frac{792675}{4398046511104}\cdot t^7+\frac{396045}{140737488355328}\cdot t^5-\frac{5863}{281474976710656}\cdot t^3+\frac{13}{281474976710656}\cdot t$

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.