Rule: Q[4, 16, 40]

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.

• $P_1$:
  $8\cdot t^4-8\cdot t^2+1$
• $P_2$:
  $8\cdot t^{20}-40\cdot t^{18}+85\cdot t^{16}-100\cdot t^{14}+\frac{2275}{32}\cdot t^{12}-\frac{1001}{32}\cdot t^{10}+\frac{2145}{256}\cdot t^8-\frac{165}{128}\cdot t^6+\frac{825}{8192}\cdot t^4-\frac{25}{8192}\cdot t^2+\frac{1}{65536}$
• $P_3$:
  $8\cdot t^{60}-120\cdot t^{58}+855\cdot t^{56}-3850\cdot t^{54}+\frac{393525}{32}\cdot t^{52}-\frac{948753}{32}\cdot t^{50}+\frac{14348425}{256}\cdot t^{48}-\frac{5453175}{64}\cdot t^{46}+\frac{434156625}{4096}\cdot t^{44}-\frac{447398875}{4096}\cdot t^{42}+\frac{3081683451}{32768}\cdot t^{40}-\frac{1114894755}{16384}\cdot t^{38}+\frac{87085668085}{2097152}\cdot t^{36}-\frac{44896866525}{2097152}\cdot t^{34}+\frac{156441876525}{16777216}\cdot t^{32}-\frac{7184738033}{2097152}\cdot t^{30}+\frac{284123731305}{268435456}\cdot t^{28}-\frac{73460171295}{268435456}\cdot t^{26}+\frac{126320400375}{2147483648}\cdot t^{24}-\frac{11188841625}{1073741824}\cdot t^{22}+\frac{103384896615}{68719476736}\cdot t^{20}-\frac{11992143075}{68719476736}\cdot t^{18}+\frac{8778937275}{549755813888}\cdot t^{16}-\frac{154740375}{137438953472}\cdot t^{14}+\frac{521532375}{8796093022208}\cdot t^{12}-\frac{19669221}{8796093022208}\cdot t^{10}+\frac{4005045}{70368744177664}\cdot t^8-\frac{31465}{35184372088832}\cdot t^6+\frac{67425}{9007199254740992}\cdot t^4-\frac{225}{9007199254740992}\cdot t^2+\frac{1}{72057594037927936}$

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.