Rule: Q[1, 68]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{69}-\frac{69}{4}\cdot t^{67}+\frac{2277}{16}\cdot t^{65}-\frac{1495}{2}\cdot t^{63}+\frac{44919}{16}\cdot t^{61}-\frac{8220177}{1024}\cdot t^{59}+\frac{74416523}{4096}\cdot t^{57}-\frac{136830381}{4096}\cdot t^{55}+\frac{3331034685}{65536}\cdot t^{53}-\frac{17000614059}{262144}\cdot t^{51}+\frac{73477230255}{1048576}\cdot t^{49}-\frac{33859413315}{524288}\cdot t^{47}+\frac{214046934465}{4194304}\cdot t^{45}-\frac{1164321236925}{33554432}\cdot t^{43}+\frac{2730862537515}{134217728}\cdot t^{41}-\frac{1382288444915}{134217728}\cdot t^{39}+\frac{19325957314755}{4294967296}\cdot t^{37}-\frac{29120107628115}{17179869184}\cdot t^{35}+\frac{37748287666075}{68719476736}\cdot t^{33}-\frac{2622512616801}{17179869184}\cdot t^{31}+\frac{4977421905357}{137438953472}\cdot t^{29}-\frac{16038359472817}{2199023255552}\cdot t^{27}+\frac{10888712137251}{8796093022208}\cdot t^{25}-\frac{1543768261425}{8796093022208}\cdot t^{23}+\frac{2893136075115}{140737488355328}\cdot t^{21}-\frac{1104651955953}{562949953421312}\cdot t^{19}+\frac{337916787957}{2251799813685248}\cdot t^{17}-\frac{10131543907}{1125899906842624}\cdot t^{15}+\frac{3706662405}{9007199254740992}\cdot t^{13}-\frac{996964371}{72057594037927936}\cdot t^{11}+\frac{93731693}{288230376151711744}\cdot t^9-\frac{1432233}{288230376151711744}\cdot t^7+\frac{812889}{18446744073709551616}\cdot t^5-\frac{13685}{73786976294838206464}\cdot t^3+\frac{69}{295147905179352825856}\cdot t$

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.