Rule: Q[7, 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.

• $P_1$:
  $128\cdot t^7-192\cdot t^5+80\cdot t^3-8\cdot t$
• $P_2$:
  $128\cdot t^{79}-2496\cdot t^{77}+23408\cdot t^{75}-140600\cdot t^{73}+607725\cdot t^{71}-\frac{4027191}{2}\cdot t^{69}+\frac{42557613}{8}\cdot t^{67}-\frac{184138713}{16}\cdot t^{65}+\frac{1329890705}{64}\cdot t^{63}-\frac{4064595535}{128}\cdot t^{61}+\frac{21252028083}{512}\cdot t^{59}-\frac{47908063307}{1024}\cdot t^{57}+\frac{374810142343}{8192}\cdot t^{55}-\frac{639027625005}{16384}\cdot t^{53}+\frac{1906017461595}{65536}\cdot t^{51}-\frac{2492484372855}{131072}\cdot t^{49}+\frac{366395202809685}{33554432}\cdot t^{47}-\frac{369816259792035}{67108864}\cdot t^{45}+\frac{656125622211675}{268435456}\cdot t^{43}-\frac{511200549488475}{536870912}\cdot t^{41}+\frac{1397281501935165}{4294967296}\cdot t^{39}-\frac{835662302610135}{8589934592}\cdot t^{37}+\frac{872337137207445}{34359738368}\cdot t^{35}-\frac{395911973027025}{68719476736}\cdot t^{33}+\frac{622147386185325}{549755813888}\cdot t^{31}-\frac{210398934237219}{1099511627776}\cdot t^{29}+\frac{121683714103007}{4398046511104}\cdot t^{27}-\frac{29846948742247}{8796093022208}\cdot t^{25}+\frac{24599133578775}{70368744177664}\cdot t^{23}-\frac{4207965378925}{140737488355328}\cdot t^{21}+\frac{1178230306099}{562949953421312}\cdot t^{19}-\frac{132638171391}{1125899906842624}\cdot t^{17}+\frac{751616304549}{144115188075855872}\cdot t^{15}-\frac{50883115395}{288230376151711744}\cdot t^{13}+\frac{5075297955}{1152921504606846976}\cdot t^{11}-\frac{177232627}{2305843009213693952}\cdot t^9+\frac{16112057}{18446744073709551616}\cdot t^7-\frac{212667}{36893488147419103232}\cdot t^5+\frac{2665}{147573952589676412928}\cdot t^3-\frac{5}{295147905179352825856}\cdot t$

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.