Rule: Q[8, 48]

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.

• $P_1$:
  $128\cdot t^8-256\cdot t^6+160\cdot t^4-32\cdot t^2+1$
• $P_2$:
  $128\cdot t^{56}-1792\cdot t^{54}+11872\cdot t^{52}-49504\cdot t^{50}+145775\cdot t^{48}-322420\cdot t^{46}+\frac{1112349}{2}\cdot t^{44}-\frac{1533939}{2}\cdot t^{42}+\frac{440240493}{512}\cdot t^{40}-\frac{202947745}{256}\cdot t^{38}+\frac{1240628389}{2048}\cdot t^{36}-\frac{789490793}{2048}\cdot t^{34}+\frac{13421343481}{65536}\cdot t^{32}-\frac{744296329}{8192}\cdot t^{30}+\frac{2202509545}{65536}\cdot t^{28}-\frac{676868787}{65536}\cdot t^{26}+\frac{43996471155}{16777216}\cdot t^{24}-\frac{4578818265}{8388608}\cdot t^{22}+\frac{6185421165}{67108864}\cdot t^{20}-\frac{835867725}{67108864}\cdot t^{18}+\frac{2841950265}{2147483648}\cdot t^{16}-\frac{57998985}{536870912}\cdot t^{14}+\frac{28224105}{4294967296}\cdot t^{12}-\frac{1227135}{4294967296}\cdot t^{10}+\frac{18407025}{2199023255552}\cdot t^8-\frac{166257}{1099511627776}\cdot t^6+\frac{12789}{8796093022208}\cdot t^4-\frac{49}{8796093022208}\cdot t^2+\frac{1}{281474976710656}$

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.