Rule: Q[16, 64]

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.

• $P_1$:
  $32768\cdot t^{16}-131072\cdot t^{14}+212992\cdot t^{12}-180224\cdot t^{10}+84480\cdot t^8-21504\cdot t^6+2688\cdot t^4-128\cdot t^2+1$
• $P_2$:
  $32768\cdot t^{80}-655360\cdot t^{78}+6307840\cdot t^{76}-38912000\cdot t^{74}+172864000\cdot t^{72}-589120512\cdot t^{70}+1602168960\cdot t^{68}-3571175040\cdot t^{66}+6649453525\cdot t^{64}-10489278800\cdot t^{62}+14168018722\cdot t^{60}-16520021830\cdot t^{58}+\frac{267721530245}{16}\cdot t^{56}-\frac{118338449075}{8}\cdot t^{54}+\frac{733083639075}{64}\cdot t^{52}-\frac{498496874571}{64}\cdot t^{50}+\frac{610658671349475}{131072}\cdot t^{48}-\frac{80394839085225}{32768}\cdot t^{46}+\frac{298238919187125}{262144}\cdot t^{44}-\frac{121714416544875}{262144}\cdot t^{42}+\frac{1397281501935165}{8388608}\cdot t^{40}-\frac{219911132265825}{4194304}\cdot t^{38}+\frac{484631742893025}{33554432}\cdot t^{36}-\frac{116444697949125}{33554432}\cdot t^{34}+\frac{3110736930926625}{4294967296}\cdot t^{32}-\frac{70132978079073}{536870912}\cdot t^{30}+\frac{86916938645005}{4294967296}\cdot t^{28}-\frac{11479595670095}{4294967296}\cdot t^{26}+\frac{40998555964625}{137438953472}\cdot t^{24}-\frac{1912711535875}{68719476736}\cdot t^{22}+\frac{1178230306099}{549755813888}\cdot t^{20}-\frac{73687872995}{549755813888}\cdot t^{18}+\frac{3758081522745}{562949953421312}\cdot t^{16}-\frac{36345082425}{140737488355328}\cdot t^{14}+\frac{8458829925}{1125899906842624}\cdot t^{12}-\frac{177232627}{1125899906842624}\cdot t^{10}+\frac{80560285}{36028797018963968}\cdot t^8-\frac{354445}{18014398509481984}\cdot t^6+\frac{13325}{144115188075855872}\cdot t^4-\frac{25}{144115188075855872}\cdot t^2+\frac{1}{18446744073709551616}$

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.