Rule: Q[3, 30, 34]

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.

• $P_1$:
  $4\cdot t^3-3\cdot t$
• $P_2$:
  $4\cdot t^{33}-33\cdot t^{31}+\frac{495}{4}\cdot t^{29}-\frac{2233}{8}\cdot t^{27}+\frac{27027}{64}\cdot t^{25}-\frac{57915}{128}\cdot t^{23}+\frac{180895}{512}\cdot t^{21}-\frac{208725}{1024}\cdot t^{19}+\frac{1427679}{16384}\cdot t^{17}-\frac{898909}{32768}\cdot t^{15}+\frac{820743}{131072}\cdot t^{13}-\frac{264537}{262144}\cdot t^{11}+\frac{230945}{2097152}\cdot t^9-\frac{31977}{4194304}\cdot t^7+\frac{5049}{16777216}\cdot t^5-\frac{187}{33554432}\cdot t^3+\frac{33}{1073741824}\cdot t$
• $P_3$:
  $4\cdot t^{67}-68\cdot t^{65}+\frac{2209}{4}\cdot t^{63}-2852\cdot t^{61}+\frac{673135}{64}\cdot t^{59}-\frac{1887233}{64}\cdot t^{57}+\frac{33451761}{512}\cdot t^{55}-\frac{30056499}{256}\cdot t^{53}+\frac{2855107827}{16384}\cdot t^{51}-\frac{3546403575}{16384}\cdot t^{49}+\frac{29776261515}{131072}\cdot t^{47}-\frac{6647420325}{32768}\cdot t^{45}+\frac{324837273215}{2097152}\cdot t^{43}-\frac{212768262805}{2097152}\cdot t^{41}+\frac{958190103325}{16777216}\cdot t^{39}-\frac{231926696085}{8388608}\cdot t^{37}+\frac{12351427293471}{1073741824}\cdot t^{35}-\frac{4409214364119}{1073741824}\cdot t^{33}+\frac{10773167031869}{8589934592}\cdot t^{31}-\frac{350450612105}{1073741824}\cdot t^{29}+\frac{9893428758983}{137438953472}\cdot t^{27}-\frac{1836512465073}{137438953472}\cdot t^{25}+\frac{2275628770545}{1099511627776}\cdot t^{23}-\frac{145467913695}{549755813888}\cdot t^{21}+\frac{969342861825}{35184372088832}\cdot t^{19}-\frac{80820408357}{35184372088832}\cdot t^{17}+\frac{42255951417}{281474976710656}\cdot t^{15}-\frac{526453501}{70368744177664}\cdot t^{13}+\frac{1234423193}{4503599627370496}\cdot t^{11}-\frac{31622635}{4503599627370496}\cdot t^9+\frac{4214419}{36028797018963968}\cdot t^7-\frac{20383}{18014398509481984}\cdot t^5+\frac{23969}{4611686018427387904}\cdot t^3-\frac{33}{4611686018427387904}\cdot t$

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.