Rule: Q[10, 77]

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.

• $P_1$:
  $1024\cdot t^{10}-2304\cdot t^8+1792\cdot t^6-560\cdot t^4+60\cdot t^2-1$
• $P_2$:
  $1024\cdot t^{87}-22016\cdot t^{85}+228480\cdot t^{83}-1524544\cdot t^{81}+7350480\cdot t^{79}-27285336\cdot t^{77}+81135054\cdot t^{75}-198544775\cdot t^{73}+\frac{26088783435}{64}\cdot t^{71}-\frac{91182316225}{128}\cdot t^{69}+\frac{548496702215}{512}\cdot t^{67}-\frac{1431790092795}{1024}\cdot t^{65}+\frac{1632743088275}{1024}\cdot t^{63}-\frac{3270510001437}{2048}\cdot t^{61}+\frac{11554118344845}{8192}\cdot t^{59}-\frac{18053969395461}{16384}\cdot t^{57}+\frac{800392643198771}{1048576}\cdot t^{55}-\frac{984741570132705}{2097152}\cdot t^{53}+\frac{2153926799433123}{8388608}\cdot t^{51}-\frac{2094780068098575}{16777216}\cdot t^{49}+\frac{3622737294241065}{67108864}\cdot t^{47}-\frac{2783353955276895}{134217728}\cdot t^{45}+\frac{3795482666286675}{536870912}\cdot t^{43}-\frac{2292522306124995}{1073741824}\cdot t^{41}+\frac{156655690918541325}{274877906944}\cdot t^{39}-\frac{73702772679770871}{549755813888}\cdot t^{37}+\frac{60900802239115881}{2199023255552}\cdot t^{35}-\frac{22001200566043685}{4398046511104}\cdot t^{33}+\frac{6914663035042301}{8796093022208}\cdot t^{31}-\frac{1879204156221315}{17592186044416}\cdot t^{29}+\frac{876961939569947}{70368744177664}\cdot t^{27}-\frac{174201268131891}{140737488355328}\cdot t^{25}+\frac{1866442158555975}{18014398509481984}\cdot t^{23}-\frac{260170725132045}{36028797018963968}\cdot t^{21}+\frac{59516178951775}{144115188075855872}\cdot t^{19}-\frac{5486397089355}{288230376151711744}\cdot t^{17}+\frac{797168807855}{1152921504606846976}\cdot t^{15}-\frac{44357564825}{2305843009213693952}\cdot t^{13}+\frac{3641989533}{9223372036854775808}\cdot t^{11}-\frac{104819165}{18446744073709551616}\cdot t^9+\frac{62891499}{1180591620717411303424}\cdot t^7-\frac{685377}{2361183241434822606848}\cdot t^5+\frac{7095}{9444732965739290427392}\cdot t^3-\frac{11}{18889465931478580854784}\cdot t$

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.