Rule: Q[2, 6, 72]

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.

• $P_1$:
  $4\cdot t^2-1$
• $P_2$:
  $4\cdot t^8-7\cdot t^6+\frac{15}{4}\cdot t^4-\frac{5}{8}\cdot t^2+\frac{1}{64}$
• $P_3$:
  $4\cdot t^{80}-79\cdot t^{78}+\frac{3003}{4}\cdot t^{76}-\frac{36575}{8}\cdot t^{74}+\frac{1282975}{64}\cdot t^{72}-\frac{8629695}{128}\cdot t^{70}+\frac{92625393}{512}\cdot t^{68}-\frac{407337153}{1024}\cdot t^{66}+\frac{11969016345}{16384}\cdot t^{64}-\frac{9309234935}{8192}\cdot t^{62}+\frac{49588065527}{32768}\cdot t^{60}-\frac{113988150627}{65536}\cdot t^{58}+\frac{910253202833}{524288}\cdot t^{56}-\frac{1585735217605}{1048576}\cdot t^{54}+\frac{4838352017895}{4194304}\cdot t^{52}-\frac{6480459369423}{8388608}\cdot t^{50}+\frac{122131734269895}{268435456}\cdot t^{48}-\frac{1012974972473835}{4294967296}\cdot t^{46}+\frac{1849081298960175}{17179869184}\cdot t^{44}-\frac{1484915881847475}{34359738368}\cdot t^{42}+\frac{4191844505805495}{274877906944}\cdot t^{40}-\frac{2594951360736735}{549755813888}\cdot t^{38}+\frac{2810864108779545}{2199023255552}\cdot t^{36}-\frac{1327469556620025}{4398046511104}\cdot t^{34}+\frac{4355031703297275}{70368744177664}\cdot t^{32}-\frac{771462758869803}{70368744177664}\cdot t^{30}+\frac{469351468683027}{281474976710656}\cdot t^{28}-\frac{121683714103007}{562949953421312}\cdot t^{26}+\frac{106596245508025}{4503599627370496}\cdot t^{24}-\frac{19509657665925}{9007199254740992}\cdot t^{22}+\frac{5891151530495}{36028797018963968}\cdot t^{20}-\frac{722141155351}{72057594037927936}\cdot t^{18}+\frac{2254848913647}{4611686018427387904}\cdot t^{16}-\frac{341643774795}{18446744073709551616}\cdot t^{14}+\frac{38910617655}{73786976294838206464}\cdot t^{12}-\frac{1595093643}{147573952589676412928}\cdot t^{10}+\frac{177232627}{1180591620717411303424}\cdot t^8-\frac{3048227}{2361183241434822606848}\cdot t^6+\frac{55965}{9444732965739290427392}\cdot t^4-\frac{205}{18889465931478580854784}\cdot t^2+\frac{1}{302231454903657293676544}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Chebyshev U (second kind) type can be downloaded here packed into a single file.