Rule: Q[4, 20, 50]

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.

• $P_1$:
  $16\cdot t^4-12\cdot t^2+1$
• $P_2$:
  $16\cdot t^{24}-92\cdot t^{22}+231\cdot t^{20}-\frac{665}{2}\cdot t^{18}+\frac{4845}{16}\cdot t^{16}-\frac{2907}{16}\cdot t^{14}+\frac{4641}{64}\cdot t^{12}-\frac{2431}{128}\cdot t^{10}+\frac{6435}{2048}\cdot t^8-\frac{5005}{16384}\cdot t^6+\frac{1001}{65536}\cdot t^4-\frac{39}{131072}\cdot t^2+\frac{1}{1048576}$
• $P_3$:
  $16\cdot t^{74}-292\cdot t^{72}+2556\cdot t^{70}-\frac{57155}{4}\cdot t^{68}+\frac{916895}{16}\cdot t^{66}-\frac{11238513}{64}\cdot t^{64}+\frac{3420417}{8}\cdot t^{62}-\frac{54353013}{64}\cdot t^{60}+\frac{717946515}{512}\cdot t^{58}-\frac{3995843735}{2048}\cdot t^{56}+\frac{4733537963}{2048}\cdot t^{54}-\frac{615790256823}{262144}\cdot t^{52}+\frac{2160153123141}{1048576}\cdot t^{50}-\frac{6566222272575}{4194304}\cdot t^{48}+\frac{2168237331225}{2097152}\cdot t^{46}-\frac{9973891723635}{16777216}\cdot t^{44}+\frac{79960182801345}{268435456}\cdot t^{42}-\frac{139646485582065}{1073741824}\cdot t^{40}+\frac{53081997443475}{1073741824}\cdot t^{38}-\frac{280576272201225}{17179869184}\cdot t^{36}+\frac{321387366339585}{68719476736}\cdot t^{34}-\frac{317986441828055}{274877906944}\cdot t^{32}+\frac{16908369977135}{68719476736}\cdot t^{30}-\frac{24599133578775}{549755813888}\cdot t^{28}+\frac{30387165009075}{4398046511104}\cdot t^{26}-\frac{15801325804719}{17592186044416}\cdot t^{24}+\frac{1711603580103}{17592186044416}\cdot t^{22}-\frac{4881239839553}{562949953421312}\cdot t^{20}+\frac{1409476549415}{2251799813685248}\cdot t^{18}-\frac{323313211485}{9007199254740992}\cdot t^{16}+\frac{7184738033}{4503599627370496}\cdot t^{14}-\frac{1917334783}{36028797018963968}\cdot t^{12}+\frac{1471442973}{1152921504606846976}\cdot t^{10}-\frac{95548245}{4611686018427387904}\cdot t^8+\frac{959595}{4611686018427387904}\cdot t^6-\frac{82251}{73786976294838206464}\cdot t^4+\frac{703}{295147905179352825856}\cdot t^2-\frac{1}{1180591620717411303424}$

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.