Rule: Q[2, 21, 48]

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.

• $P_1$:
  $4\cdot t^2-1$
• $P_2$:
  $4\cdot t^{23}-22\cdot t^{21}+\frac{105}{2}\cdot t^{19}-\frac{285}{4}\cdot t^{17}+\frac{969}{16}\cdot t^{15}-\frac{1071}{32}\cdot t^{13}+\frac{1547}{128}\cdot t^{11}-\frac{715}{256}\cdot t^9+\frac{6435}{16384}\cdot t^7-\frac{1001}{32768}\cdot t^5+\frac{143}{131072}\cdot t^3-\frac{3}{262144}\cdot t$
• $P_3$:
  $4\cdot t^{71}-70\cdot t^{69}+\frac{1173}{2}\cdot t^{67}-\frac{12529}{4}\cdot t^{65}+\frac{47905}{4}\cdot t^{63}-\frac{279279}{8}\cdot t^{61}+\frac{2581215}{32}\cdot t^{59}-\frac{9706503}{64}\cdot t^{57}+\frac{3872894697}{16384}\cdot t^{55}-\frac{10143295635}{32768}\cdot t^{53}+\frac{45088585113}{131072}\cdot t^{51}-\frac{85675031325}{262144}\cdot t^{49}+\frac{279871768995}{1048576}\cdot t^{47}-\frac{394447695285}{2097152}\cdot t^{45}+\frac{961830587025}{8388608}\cdot t^{43}-\frac{1015828093665}{16777216}\cdot t^{41}+\frac{29749251314475}{1073741824}\cdot t^{39}-\frac{23576679383985}{2147483648}\cdot t^{37}+\frac{32308782859535}{8589934592}\cdot t^{35}-\frac{19090095135475}{17179869184}\cdot t^{33}+\frac{9691894453395}{34359738368}\cdot t^{31}-\frac{4207965378925}{68719476736}\cdot t^{29}+\frac{3106243534261}{274877906944}\cdot t^{27}-\frac{967428110493}{549755813888}\cdot t^{25}+\frac{8061900920775}{35184372088832}\cdot t^{23}-\frac{1735881645069}{70368744177664}\cdot t^{21}+\frac{609590544255}{281474976710656}\cdot t^{19}-\frac{85794224747}{562949953421312}\cdot t^{17}+\frac{18941582087}{2251799813685248}\cdot t^{15}-\frac{1594920705}{4503599627370496}\cdot t^{13}+\frac{197466373}{18014398509481984}\cdot t^{11}-\frac{8544965}{36028797018963968}\cdot t^9+\frac{15380937}{4611686018427387904}\cdot t^7-\frac{250971}{9223372036854775808}\cdot t^5+\frac{3885}{36893488147419103232}\cdot t^3-\frac{9}{73786976294838206464}\cdot t$

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.