Rule: Q[6, 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.

• $P_1$:
  $32\cdot t^6-48\cdot t^4+18\cdot t^2-1$
• $P_2$:
  $32\cdot t^{54}-432\cdot t^{52}+2754\cdot t^{50}-11025\cdot t^{48}+\frac{62181}{2}\cdot t^{46}-\frac{262683}{4}\cdot t^{44}+\frac{13805451}{128}\cdot t^{42}-\frac{36129159}{256}\cdot t^{40}+\frac{306312435}{2048}\cdot t^{38}-\frac{531697881}{4096}\cdot t^{36}+\frac{3045178773}{32768}\cdot t^{34}-\frac{3611723661}{65536}\cdot t^{32}+\frac{1777197357}{65536}\cdot t^{30}-\frac{1450433115}{131072}\cdot t^{28}+\frac{7832338821}{2097152}\cdot t^{26}-\frac{4351299345}{4194304}\cdot t^{24}+\frac{15802087095}{67108864}\cdot t^{22}-\frac{5803310205}{134217728}\cdot t^{20}+\frac{6806351475}{1073741824}\cdot t^{18}-\frac{1565972595}{2147483648}\cdot t^{16}+\frac{276348105}{4294967296}\cdot t^{14}-\frac{36288135}{8589934592}\cdot t^{12}+\frac{108864405}{549755813888}\cdot t^{10}-\frac{6870825}{1099511627776}\cdot t^8+\frac{1068795}{8796093022208}\cdot t^6-\frac{22113}{17592186044416}\cdot t^4+\frac{729}{140737488355328}\cdot t^2-\frac{1}{281474976710656}$

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.