Rule: Q[1, 10, 12, 66]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{11}-\frac{11}{4}\cdot t^9+\frac{11}{4}\cdot t^7-\frac{77}{64}\cdot t^5+\frac{55}{256}\cdot t^3-\frac{11}{1024}\cdot t$
• $P_3$:
  $t^{23}-6\cdot t^{21}+\frac{251}{16}\cdot t^{19}-\frac{375}{16}\cdot t^{17}+\frac{1411}{64}\cdot t^{15}-\frac{217}{16}\cdot t^{13}+\frac{22477}{4096}\cdot t^{11}-\frac{5863}{4096}\cdot t^9+\frac{15015}{65536}\cdot t^7-\frac{671}{32768}\cdot t^5+\frac{891}{1048576}\cdot t^3-\frac{11}{1048576}\cdot t$
• $P_4$:
  $t^{89}-\frac{45}{2}\cdot t^{87}+\frac{1957}{8}\cdot t^{85}-\frac{27391}{16}\cdot t^{83}+\frac{554689}{64}\cdot t^{81}-\frac{4329477}{128}\cdot t^{79}+\frac{54210195}{512}\cdot t^{77}-\frac{279679829}{1024}\cdot t^{75}+\frac{38795649035}{65536}\cdot t^{73}-\frac{143359883095}{131072}\cdot t^{71}+\frac{913225967115}{524288}\cdot t^{69}-\frac{2528783497225}{1048576}\cdot t^{67}+\frac{1532266590535}{524288}\cdot t^{65}-\frac{6535996177987}{2097152}\cdot t^{63}+\frac{24636158350593}{8388608}\cdot t^{61}-\frac{41162206085151}{16777216}\cdot t^{59}+\frac{1955846684508275}{1073741824}\cdot t^{57}-\frac{2585526856530247}{2147483648}\cdot t^{55}+\frac{6092893079963943}{8589934592}\cdot t^{53}-\frac{6402633666964821}{17179869184}\cdot t^{51}+\frac{12001857566635365}{68719476736}\cdot t^{49}-\frac{10028828543759025}{137438953472}\cdot t^{47}+\frac{14928898487394255}{549755813888}\cdot t^{45}-\frac{9883487638698345}{1099511627776}\cdot t^{43}+\frac{743541401286540045}{281474976710656}\cdot t^{41}-\frac{387014154516853521}{562949953421312}\cdot t^{39}+\frac{355711892958199365}{2251799813685248}\cdot t^{37}-\frac{143802805044275447}{4503599627370496}\cdot t^{35}+\frac{50917064167129671}{9007199254740992}\cdot t^{33}-\frac{15708530226305917}{18014398509481984}\cdot t^{31}+\frac{8393778564455207}{72057594037927936}\cdot t^{29}-\frac{1928125147271785}{144115188075855872}\cdot t^{27}+\frac{24164204479438023}{18446744073709551616}\cdot t^{25}-\frac{3993055042243995}{36893488147419103232}\cdot t^{23}+\frac{1100199079479955}{147573952589676412928}\cdot t^{21}-\frac{124518754992905}{295147905179352825856}\cdot t^{19}+\frac{22742757165275}{1180591620717411303424}\cdot t^{17}-\frac{1638695180535}{2361183241434822606848}\cdot t^{15}+\frac{181072248833}{9444732965739290427392}\cdot t^{13}-\frac{7388798231}{18889465931478580854784}\cdot t^{11}+\frac{6771318059}{1208925819614629174706176}\cdot t^9-\frac{126468375}{2417851639229258349412352}\cdot t^7+\frac{2748603}{9671406556917033397649408}\cdot t^5-\frac{14201}{19342813113834066795298816}\cdot t^3+\frac{11}{19342813113834066795298816}\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.