Rule: Q[1, 30, 32]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{31}-\frac{31}{4}\cdot t^{29}+\frac{217}{8}\cdot t^{27}-\frac{3627}{64}\cdot t^{25}+\frac{10075}{128}\cdot t^{23}-\frac{39215}{512}\cdot t^{21}+\frac{54901}{1024}\cdot t^{19}-\frac{447051}{16384}\cdot t^{17}+\frac{330429}{32768}\cdot t^{15}-\frac{350455}{131072}\cdot t^{13}+\frac{130169}{262144}\cdot t^{11}-\frac{130169}{2097152}\cdot t^9+\frac{20553}{4194304}\cdot t^7-\frac{3689}{16777216}\cdot t^5+\frac{155}{33554432}\cdot t^3-\frac{31}{1073741824}\cdot t$
• $P_3$:
  $t^{63}-16\cdot t^{61}+\frac{1951}{16}\cdot t^{59}-\frac{9425}{16}\cdot t^{57}+\frac{259217}{128}\cdot t^{55}-\frac{337491}{64}\cdot t^{53}+\frac{44268939}{4096}\cdot t^{51}-\frac{73264815}{4096}\cdot t^{49}+\frac{797362475}{32768}\cdot t^{47}-\frac{225761445}{8192}\cdot t^{45}+\frac{13747006735}{524288}\cdot t^{43}-\frac{11058073285}{524288}\cdot t^{41}+\frac{60419672509}{4194304}\cdot t^{39}-\frac{17561974645}{2097152}\cdot t^{37}+\frac{1113356771979}{268435456}\cdot t^{35}-\frac{469578464931}{268435456}\cdot t^{33}+\frac{1346790732573}{2147483648}\cdot t^{31}-\frac{51138429529}{268435456}\cdot t^{29}+\frac{1676887120055}{34359738368}\cdot t^{27}-\frac{360026437953}{34359738368}\cdot t^{25}+\frac{514057545105}{274877906944}\cdot t^{23}-\frac{37743692415}{137438953472}\cdot t^{21}+\frac{288075375705}{8796093022208}\cdot t^{19}-\frac{27444469725}{8796093022208}\cdot t^{17}+\frac{16361903385}{70368744177664}\cdot t^{15}-\frac{232041789}{17592186044416}\cdot t^{13}+\frac{618457161}{1125899906842624}\cdot t^{11}-\frac{17988091}{1125899906842624}\cdot t^9+\frac{2719475}{9007199254740992}\cdot t^7-\frac{14911}{4503599627370496}\cdot t^5+\frac{19871}{1152921504606846976}\cdot t^3-\frac{31}{1152921504606846976}\cdot t$

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.