Rule: Q[4, 64]

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.

• $P_1$:
  $8\cdot t^4-8\cdot t^2+1$
• $P_2$:
  $8\cdot t^{68}-136\cdot t^{66}+1105\cdot t^{64}-5712\cdot t^{62}+\frac{675087}{32}\cdot t^{60}-\frac{1896673}{32}\cdot t^{58}+\frac{33711833}{256}\cdot t^{56}-\frac{30395915}{128}\cdot t^{54}+\frac{2899770291}{8192}\cdot t^{52}-\frac{3620617143}{8192}\cdot t^{50}+\frac{30587972415}{65536}\cdot t^{48}-\frac{6878634945}{16384}\cdot t^{46}+\frac{339018436575}{1048576}\cdot t^{44}-\frac{224273734965}{1048576}\cdot t^{42}+\frac{1021691459285}{8388608}\cdot t^{40}-\frac{250603565485}{4194304}\cdot t^{38}+\frac{13551869733535}{536870912}\cdot t^{36}-\frac{4923689695575}{536870912}\cdot t^{34}+\frac{12276399640967}{4294967296}\cdot t^{32}-\frac{408773779667}{536870912}\cdot t^{30}+\frac{11854439610343}{68719476736}\cdot t^{28}-\frac{2269999074321}{68719476736}\cdot t^{26}+\frac{2916006716025}{549755813888}\cdot t^{24}-\frac{194400447735}{274877906944}\cdot t^{22}+\frac{1360803134145}{17592186044416}\cdot t^{20}-\frac{120257021157}{17592186044416}\cdot t^{18}+\frac{67396792077}{140737488355328}\cdot t^{16}-\frac{913235665}{35184372088832}\cdot t^{14}+\frac{2374412729}{2251799813685248}\cdot t^{12}-\frac{69279947}{2251799813685248}\cdot t^{10}+\frac{10938939}{18014398509481984}\cdot t^8-\frac{66759}{9007199254740992}\cdot t^6+\frac{111265}{2305843009213693952}\cdot t^4-\frac{289}{2305843009213693952}\cdot t^2+\frac{1}{18446744073709551616}$

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.