Rule: Q[2, 20, 67]

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.

• $P_1$:
  $2\cdot t^2-1$
• $P_2$:
  $2\cdot t^{22}-11\cdot t^{20}+\frac{209}{8}\cdot t^{18}-\frac{561}{16}\cdot t^{16}+\frac{935}{32}\cdot t^{14}-\frac{1001}{64}\cdot t^{12}+\frac{11011}{2048}\cdot t^{10}-\frac{4719}{4096}\cdot t^8+\frac{4719}{32768}\cdot t^6-\frac{605}{65536}\cdot t^4+\frac{121}{524288}\cdot t^2-\frac{1}{1048576}$
• $P_3$:
  $2\cdot t^{89}-45\cdot t^{87}+\frac{1957}{4}\cdot t^{85}-\frac{27391}{8}\cdot t^{83}+\frac{554689}{32}\cdot t^{81}-\frac{4329477}{64}\cdot t^{79}+\frac{54210195}{256}\cdot t^{77}-\frac{279679829}{512}\cdot t^{75}+\frac{38795649035}{32768}\cdot t^{73}-\frac{143359883095}{65536}\cdot t^{71}+\frac{913225967115}{262144}\cdot t^{69}-\frac{2528783497225}{524288}\cdot t^{67}+\frac{1532266590535}{262144}\cdot t^{65}-\frac{6535996177987}{1048576}\cdot t^{63}+\frac{24636158350593}{4194304}\cdot t^{61}-\frac{41162206085151}{8388608}\cdot t^{59}+\frac{1955846684508275}{536870912}\cdot t^{57}-\frac{2585526856530247}{1073741824}\cdot t^{55}+\frac{6092893079963943}{4294967296}\cdot t^{53}-\frac{6402633666964821}{8589934592}\cdot t^{51}+\frac{12001857566635365}{34359738368}\cdot t^{49}-\frac{10028828543759025}{68719476736}\cdot t^{47}+\frac{14928898487394255}{274877906944}\cdot t^{45}-\frac{9883487638698345}{549755813888}\cdot t^{43}+\frac{743541401286540045}{140737488355328}\cdot t^{41}-\frac{387014154516853521}{281474976710656}\cdot t^{39}+\frac{355711892958199365}{1125899906842624}\cdot t^{37}-\frac{143802805044275447}{2251799813685248}\cdot t^{35}+\frac{50917064167129671}{4503599627370496}\cdot t^{33}-\frac{15708530226305917}{9007199254740992}\cdot t^{31}+\frac{8393778564455207}{36028797018963968}\cdot t^{29}-\frac{1928125147271785}{72057594037927936}\cdot t^{27}+\frac{24164204479438023}{9223372036854775808}\cdot t^{25}-\frac{3993055042243995}{18446744073709551616}\cdot t^{23}+\frac{1100199079479955}{73786976294838206464}\cdot t^{21}-\frac{124518754992905}{147573952589676412928}\cdot t^{19}+\frac{22742757165275}{590295810358705651712}\cdot t^{17}-\frac{1638695180535}{1180591620717411303424}\cdot t^{15}+\frac{181072248833}{4722366482869645213696}\cdot t^{13}-\frac{7388798231}{9444732965739290427392}\cdot t^{11}+\frac{6771318059}{604462909807314587353088}\cdot t^9-\frac{126468375}{1208925819614629174706176}\cdot t^7+\frac{2748603}{4835703278458516698824704}\cdot t^5-\frac{14201}{9671406556917033397649408}\cdot t^3+\frac{11}{9671406556917033397649408}\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.