Rule: Q[1, 8, 100]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^9-4\cdot t^7+\frac{21}{8}\cdot t^5-\frac{5}{8}\cdot t^3+\frac{5}{128}\cdot t$
• $P_3$:
  $2\cdot t^{109}-54\cdot t^{107}+\frac{5671}{8}\cdot t^{105}-\frac{24115}{4}\cdot t^{103}+\frac{2390115}{64}\cdot t^{101}-\frac{11495315}{64}\cdot t^{99}+\frac{1429840335}{2048}\cdot t^{97}-\frac{577092285}{256}\cdot t^{95}+\frac{50523863775}{8192}\cdot t^{93}-\frac{118889488025}{8192}\cdot t^{91}+\frac{3894819627699}{131072}\cdot t^{89}-\frac{3501403503689}{65536}\cdot t^{87}+\frac{89107146308167}{1048576}\cdot t^{85}-\frac{126135016780395}{1048576}\cdot t^{83}+\frac{20439879147794485}{134217728}\cdot t^{81}-\frac{5809228810425801}{33554432}\cdot t^{79}+\frac{380813488615359423}{2147483648}\cdot t^{77}-\frac{352390976498590029}{2147483648}\cdot t^{75}+\frac{4724081931321677925}{34359738368}\cdot t^{73}-\frac{1795096488651441525}{17179869184}\cdot t^{71}+\frac{19825843441328143065}{274877906944}\cdot t^{69}-\frac{12442864824332751105}{274877906944}\cdot t^{67}+\frac{227365075426443906555}{8796093022208}\cdot t^{65}-\frac{7385672115301776075}{549755813888}\cdot t^{63}+\frac{111815640629336191275}{17592186044416}\cdot t^{61}-\frac{48146499376867112949}{17592186044416}\cdot t^{59}+\frac{301753334922416228043}{281474976710656}\cdot t^{57}-\frac{53725828038395392677}{140737488355328}\cdot t^{55}+\frac{277989040547098111935}{2251799813685248}\cdot t^{53}-\frac{81538718151107109035}{2251799813685248}\cdot t^{51}+\frac{1386158208568820853595}{144115188075855872}\cdot t^{49}-\frac{83203453107234244785}{36028797018963968}\cdot t^{47}+\frac{2306229046382569708015}{4611686018427387904}\cdot t^{45}-\frac{449265398645955137925}{4611686018427387904}\cdot t^{43}+\frac{1255995835843026283425}{73786976294838206464}\cdot t^{41}-\frac{98087293846788719277}{36893488147419103232}\cdot t^{39}+\frac{218266320541953276229}{590295810358705651712}\cdot t^{37}-\frac{26909546368186020357}{590295810358705651712}\cdot t^{35}+\frac{93632632099828550365}{18889465931478580854784}\cdot t^{33}-\frac{1115881856010957805}{2361183241434822606848}\cdot t^{31}+\frac{2965057503114830739}{75557863725914323419136}\cdot t^{29}-\frac{212763051655111573}{75557863725914323419136}\cdot t^{27}+\frac{209187202047462639}{1208925819614629174706176}\cdot t^{25}-\frac{5445692521193925}{604462909807314587353088}\cdot t^{23}+\frac{3795482666286675}{9671406556917033397649408}\cdot t^{21}-\frac{136248095712855}{9671406556917033397649408}\cdot t^{19}+\frac{1012974972473835}{2475880078570760549798248448}\cdot t^{17}-\frac{5815796869995}{618970019642690137449562112}\cdot t^{15}+\frac{6566222272575}{39614081257132168796771975168}\cdot t^{13}-\frac{85675031325}{39614081257132168796771975168}\cdot t^{11}+\frac{12565671261}{633825300114114700748351602688}\cdot t^9-\frac{37584261}{316912650057057350374175801344}\cdot t^7+\frac{2093553}{5070602400912917605986812821504}\cdot t^5-\frac{3465}{5070602400912917605986812821504}\cdot t^3+\frac{55}{162259276829213363391578010288128}\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.