Rule: Q[1, 80]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{81}-40\cdot t^{79}+\frac{3081}{8}\cdot t^{77}-\frac{19019}{8}\cdot t^{75}+\frac{1353275}{128}\cdot t^{73}-\frac{2309355}{64}\cdot t^{71}+\frac{100679775}{1024}\cdot t^{69}-\frac{224947383}{1024}\cdot t^{67}+\frac{13442126049}{32768}\cdot t^{65}-\frac{1329890705}{2048}\cdot t^{63}+\frac{57717256597}{65536}\cdot t^{61}-\frac{67620089355}{65536}\cdot t^{59}+\frac{1101885456061}{1048576}\cdot t^{57}-\frac{490136339987}{524288}\cdot t^{55}+\frac{6116407267905}{8388608}\cdot t^{53}-\frac{4193238415509}{8388608}\cdot t^{51}+\frac{162011484235575}{536870912}\cdot t^{49}-\frac{21552658988805}{134217728}\cdot t^{47}+\frac{2588713818544245}{34359738368}\cdot t^{45}-\frac{1070520752029575}{34359738368}\cdot t^{43}+\frac{6236646703759395}{549755813888}\cdot t^{41}-\frac{998058215667975}{274877906944}\cdot t^{39}+\frac{4482188713999815}{4398046511104}\cdot t^{37}-\frac{1099903346913735}{4398046511104}\cdot t^{35}+\frac{7522327487513475}{140737488355328}\cdot t^{33}-\frac{174201268131891}{17592186044416}\cdot t^{31}+\frac{890149337157465}{562949953421312}\cdot t^{29}-\frac{121683714103007}{562949953421312}\cdot t^{27}+\frac{225984040477013}{9007199254740992}\cdot t^{25}-\frac{11027197811175}{4503599627370496}\cdot t^{23}+\frac{14307082288345}{72057594037927936}\cdot t^{21}-\frac{950185730725}{72057594037927936}\cdot t^{19}+\frac{6499270398159}{9223372036854775808}\cdot t^{17}-\frac{68328754959}{2305843009213693952}\cdot t^{15}+\frac{140676848445}{147573952589676412928}\cdot t^{13}-\frac{3335195799}{147573952589676412928}\cdot t^{11}+\frac{886163135}{2361183241434822606848}\cdot t^9-\frac{4790071}{1180591620717411303424}\cdot t^7+\frac{481299}{18889465931478580854784}\cdot t^5-\frac{1435}{18889465931478580854784}\cdot t^3+\frac{41}{604462909807314587353088}\cdot t$

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.