Rule: Q[4, 24, 56]

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.

• $P_1$:
  $8\cdot t^4-8\cdot t^2+1$
• $P_2$:
  $8\cdot t^{28}-56\cdot t^{26}+175\cdot t^{24}-322\cdot t^{22}+\frac{12397}{32}\cdot t^{20}-\frac{10241}{32}\cdot t^{18}+\frac{47481}{256}\cdot t^{16}-\frac{4845}{64}\cdot t^{14}+\frac{88179}{4096}\cdot t^{12}-\frac{17017}{4096}\cdot t^{10}+\frac{17017}{32768}\cdot t^8-\frac{637}{16384}\cdot t^6+\frac{3185}{2097152}\cdot t^4-\frac{49}{2097152}\cdot t^2+\frac{1}{16777216}$
• $P_3$:
  $8\cdot t^{84}-168\cdot t^{82}+1701\cdot t^{80}-11060\cdot t^{78}+\frac{1660659}{32}\cdot t^{76}-\frac{5990985}{32}\cdot t^{74}+\frac{138304705}{256}\cdot t^{72}-\frac{163964205}{128}\cdot t^{70}+\frac{20840713425}{8192}\cdot t^{68}-\frac{35166774209}{8192}\cdot t^{66}+\frac{407744490153}{65536}\cdot t^{64}-\frac{31989916413}{4096}\cdot t^{62}+\frac{2240478960629}{262144}\cdot t^{60}-\frac{2148238223355}{262144}\cdot t^{58}+\frac{14494031768187}{2097152}\cdot t^{56}-\frac{5391499739857}{1048576}\cdot t^{54}+\frac{453837419278551}{134217728}\cdot t^{52}-\frac{264174020177067}{134217728}\cdot t^{50}+\frac{1089606648878475}{1073741824}\cdot t^{48}-\frac{124400435216085}{268435456}\cdot t^{46}+\frac{25750890089729595}{137438953472}\cdot t^{44}-\frac{9206478467454345}{137438953472}\cdot t^{42}+\frac{23245683168557745}{1099511627776}\cdot t^{40}-\frac{3230868294988425}{549755813888}\cdot t^{38}+\frac{50473342475041395}{35184372088832}\cdot t^{36}-\frac{10779052799754603}{35184372088832}\cdot t^{34}+\frac{16039916765682579}{281474976710656}\cdot t^{32}-\frac{323091240894191}{35184372088832}\cdot t^{30}+\frac{2868258975285165}{2251799813685248}\cdot t^{28}-\frac{339875201460123}{2251799813685248}\cdot t^{26}+\frac{272739359196395}{18014398509481984}\cdot t^{24}-\frac{11454057081285}{9007199254740992}\cdot t^{22}+\frac{203529783521295}{2305843009213693952}\cdot t^{20}-\frac{11488609289675}{2305843009213693952}\cdot t^{18}+\frac{4135899344283}{18446744073709551616}\cdot t^{16}-\frac{36174046743}{4611686018427387904}\cdot t^{14}+\frac{121919935319}{590295810358705651712}\cdot t^{12}-\frac{2313604293}{590295810358705651712}\cdot t^{10}+\frac{238243005}{4722366482869645213696}\cdot t^8-\frac{950257}{2361183241434822606848}\cdot t^6+\frac{259161}{151115727451828646838272}\cdot t^4-\frac{441}{151115727451828646838272}\cdot t^2+\frac{1}{1208925819614629174706176}$

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.