Rule: Q[1, 36, 38]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{37}-18\cdot t^{35}+\frac{595}{8}\cdot t^{33}-187\cdot t^{31}+\frac{5115}{16}\cdot t^{29}-\frac{6293}{16}\cdot t^{27}+\frac{736281}{2048}\cdot t^{25}-\frac{254475}{1024}\cdot t^{23}+\frac{4292145}{32768}\cdot t^{21}-\frac{1726725}{32768}\cdot t^{19}+\frac{8436285}{524288}\cdot t^{17}-\frac{482885}{131072}\cdot t^{15}+\frac{1300075}{2097152}\cdot t^{13}-\frac{156009}{2097152}\cdot t^{11}+\frac{408595}{67108864}\cdot t^9-\frac{10659}{33554432}\cdot t^7+\frac{20349}{2147483648}\cdot t^5-\frac{285}{2147483648}\cdot t^3+\frac{19}{34359738368}\cdot t$
• $P_3$:
  $2\cdot t^{75}-37\cdot t^{73}+\frac{657}{2}\cdot t^{71}-\frac{7455}{4}\cdot t^{69}+\frac{971635}{128}\cdot t^{67}-\frac{6051507}{256}\cdot t^{65}+\frac{3746171}{64}\cdot t^{63}-\frac{15147561}{128}\cdot t^{61}+\frac{815295195}{4096}\cdot t^{59}-\frac{2313383215}{8192}\cdot t^{57}+\frac{5594181229}{16384}\cdot t^{55}-\frac{11618684091}{32768}\cdot t^{53}+\frac{2668424446233}{8388608}\cdot t^{51}-\frac{4154140621425}{16777216}\cdot t^{49}+\frac{2814095259675}{16777216}\cdot t^{47}-\frac{3324630574545}{33554432}\cdot t^{45}+\frac{109712808959985}{2147483648}\cdot t^{43}-\frac{98774343460485}{4294967296}\cdot t^{41}+\frac{77581380878925}{8589934592}\cdot t^{39}-\frac{53081997443475}{17179869184}\cdot t^{37}+\frac{505037289962205}{549755813888}\cdot t^{35}-\frac{260170725132045}{1099511627776}\cdot t^{33}+\frac{28907858348005}{549755813888}\cdot t^{31}-\frac{11027197811175}{1099511627776}\cdot t^{29}+\frac{57397978350475}{35184372088832}\cdot t^{27}-\frac{15801325804719}{70368744177664}\cdot t^{25}+\frac{3646459801089}{140737488355328}\cdot t^{23}-\frac{697319977079}{281474976710656}\cdot t^{21}+\frac{3486599885395}{18014398509481984}\cdot t^{19}-\frac{437423756715}{36028797018963968}\cdot t^{17}+\frac{21554214099}{36028797018963968}\cdot t^{15}-\frac{1622360201}{72057594037927936}\cdot t^{13}+\frac{5752004349}{9223372036854775808}\cdot t^{11}-\frac{222945905}{18446744073709551616}\cdot t^9+\frac{5620485}{36893488147419103232}\cdot t^7-\frac{82251}{73786976294838206464}\cdot t^5+\frac{9139}{2361183241434822606848}\cdot t^3-\frac{19}{4722366482869645213696}\cdot t$

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.