Rule: Q[12, 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.

• $P_1$:
  $2048\cdot t^{12}-6144\cdot t^{10}+6912\cdot t^8-3584\cdot t^6+840\cdot t^4-72\cdot t^2+1$
• $P_2$:
  $2048\cdot t^{84}-43008\cdot t^{82}+435456\cdot t^{80}-2831360\cdot t^{78}+13285272\cdot t^{76}-47927880\cdot t^{74}+138304705\cdot t^{72}-327928410\cdot t^{70}+\frac{20840713425}{32}\cdot t^{68}-\frac{35166774209}{32}\cdot t^{66}+\frac{407744490153}{256}\cdot t^{64}-\frac{31989916413}{16}\cdot t^{62}+\frac{2240478960629}{1024}\cdot t^{60}-\frac{2148238223355}{1024}\cdot t^{58}+\frac{14494031768187}{8192}\cdot t^{56}-\frac{5391499739857}{4096}\cdot t^{54}+\frac{453837419278551}{524288}\cdot t^{52}-\frac{264174020177067}{524288}\cdot t^{50}+\frac{1089606648878475}{4194304}\cdot t^{48}-\frac{124400435216085}{1048576}\cdot t^{46}+\frac{25750890089729595}{536870912}\cdot t^{44}-\frac{9206478467454345}{536870912}\cdot t^{42}+\frac{23245683168557745}{4294967296}\cdot t^{40}-\frac{3230868294988425}{2147483648}\cdot t^{38}+\frac{50473342475041395}{137438953472}\cdot t^{36}-\frac{10779052799754603}{137438953472}\cdot t^{34}+\frac{16039916765682579}{1099511627776}\cdot t^{32}-\frac{323091240894191}{137438953472}\cdot t^{30}+\frac{2868258975285165}{8796093022208}\cdot t^{28}-\frac{339875201460123}{8796093022208}\cdot t^{26}+\frac{272739359196395}{70368744177664}\cdot t^{24}-\frac{11454057081285}{35184372088832}\cdot t^{22}+\frac{203529783521295}{9007199254740992}\cdot t^{20}-\frac{11488609289675}{9007199254740992}\cdot t^{18}+\frac{4135899344283}{72057594037927936}\cdot t^{16}-\frac{36174046743}{18014398509481984}\cdot t^{14}+\frac{121919935319}{2305843009213693952}\cdot t^{12}-\frac{2313604293}{2305843009213693952}\cdot t^{10}+\frac{238243005}{18446744073709551616}\cdot t^8-\frac{950257}{9223372036854775808}\cdot t^6+\frac{259161}{590295810358705651712}\cdot t^4-\frac{441}{590295810358705651712}\cdot t^2+\frac{1}{4722366482869645213696}$

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.