Rule: Q[4, 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.

• $P_1$:
  $8\cdot t^4-8\cdot t^2+1$
• $P_2$:
  $8\cdot t^{52}-104\cdot t^{50}+637\cdot t^{48}-2444\cdot t^{46}+\frac{210795}{32}\cdot t^{44}-\frac{424281}{32}\cdot t^{42}+\frac{5294289}{256}\cdot t^{40}-\frac{3277417}{128}\cdot t^{38}+\frac{209456741}{8192}\cdot t^{36}-\frac{170488045}{8192}\cdot t^{34}+\frac{910893269}{65536}\cdot t^{32}-\frac{62611289}{8192}\cdot t^{30}+\frac{1815727381}{524288}\cdot t^{28}-\frac{676868787}{524288}\cdot t^{26}+\frac{1654002675}{4194304}\cdot t^{24}-\frac{205632765}{2097152}\cdot t^{22}+\frac{5277907635}{268435456}\cdot t^{20}-\frac{842691135}{268435456}\cdot t^{18}+\frac{842691135}{2147483648}\cdot t^{16}-\frac{20160075}{536870912}\cdot t^{14}+\frac{366913365}{137438953472}\cdot t^{12}-\frac{18599295}{137438953472}\cdot t^{10}+\frac{5072535}{1099511627776}\cdot t^8-\frac{53235}{549755813888}\cdot t^6+\frac{38025}{35184372088832}\cdot t^4-\frac{169}{35184372088832}\cdot t^2+\frac{1}{281474976710656}$

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.