Rule: Q[7, 8, 14, 28]

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.

• $P_1$:
  $64\cdot t^7-112\cdot t^5+56\cdot t^3-7\cdot t$
• $P_2$:
  $64\cdot t^{15}-256\cdot t^{13}+412\cdot t^{11}-340\cdot t^9+\frac{303}{2}\cdot t^7-35\cdot t^5+\frac{231}{64}\cdot t^3-\frac{7}{64}\cdot t$
• $P_3$:
  $64\cdot t^{29}-480\cdot t^{27}+1616\cdot t^{25}-3224\cdot t^{23}+\frac{16951}{4}\cdot t^{21}-\frac{30877}{8}\cdot t^{19}+\frac{9975}{4}\cdot t^{17}-\frac{18411}{16}\cdot t^{15}+\frac{192831}{512}\cdot t^{13}-\frac{87737}{1024}\cdot t^{11}+\frac{26741}{2048}\cdot t^9-\frac{5135}{4096}\cdot t^7+\frac{17927}{262144}\cdot t^5-\frac{917}{524288}\cdot t^3+\frac{7}{524288}\cdot t$
• $P_4$:
  $64\cdot t^{57}-928\cdot t^{55}+6376\cdot t^{53}-27612\cdot t^{51}+84575\cdot t^{49}-\frac{389795}{2}\cdot t^{47}+\frac{2807357}{8}\cdot t^{45}-\frac{8097771}{16}\cdot t^{43}+\frac{608973783}{1024}\cdot t^{41}-\frac{1179773155}{2048}\cdot t^{39}+\frac{3798526303}{8192}\cdot t^{37}-\frac{5107522069}{16384}\cdot t^{35}+\frac{5752004349}{32768}\cdot t^{33}-\frac{5429590271}{65536}\cdot t^{31}+\frac{8582192365}{262144}\cdot t^{29}-\frac{5662061123}{524288}\cdot t^{27}+\frac{99306320607}{33554432}\cdot t^{25}-\frac{44906546835}{67108864}\cdot t^{23}+\frac{33199301355}{268435456}\cdot t^{21}-\frac{9911003025}{536870912}\cdot t^{19}+\frac{4704741195}{2147483648}\cdot t^{17}-\frac{869984775}{4294967296}\cdot t^{15}+\frac{244091985}{17179869184}\cdot t^{13}-\frac{25068615}{34359738368}\cdot t^{11}+\frac{114824775}{4398046511104}\cdot t^9-\frac{5330403}{8796093022208}\cdot t^7+\frac{286839}{35184372088832}\cdot t^5-\frac{3661}{70368744177664}\cdot t^3+\frac{7}{70368744177664}\cdot t$

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.