Rule: Q[18, 19, 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.

• $P_1$:
  $262144\cdot t^{18}-1114112\cdot t^{16}+1966080\cdot t^{14}-1863680\cdot t^{12}+1025024\cdot t^{10}-329472\cdot t^8+59136\cdot t^6-5280\cdot t^4+180\cdot t^2-1$
• $P_2$:
  $262144\cdot t^{37}-2359296\cdot t^{35}+9748480\cdot t^{33}-24510464\cdot t^{31}+41902080\cdot t^{29}-51552256\cdot t^{27}+47121984\cdot t^{25}-32572800\cdot t^{23}+17168580\cdot t^{21}-6906900\cdot t^{19}+\frac{8436285}{4}\cdot t^{17}-482885\cdot t^{15}+\frac{1300075}{16}\cdot t^{13}-\frac{156009}{16}\cdot t^{11}+\frac{408595}{512}\cdot t^9-\frac{10659}{256}\cdot t^7+\frac{20349}{16384}\cdot t^5-\frac{285}{16384}\cdot t^3+\frac{19}{262144}\cdot t$
• $P_3$:
  $262144\cdot t^{75}-4849664\cdot t^{73}+43057152\cdot t^{71}-244285440\cdot t^{69}+994954240\cdot t^{67}-3098371584\cdot t^{65}+7672158208\cdot t^{63}-15511102464\cdot t^{61}+26089446240\cdot t^{59}-37014131440\cdot t^{57}+44753449832\cdot t^{55}-46474736364\cdot t^{53}+\frac{2668424446233}{64}\cdot t^{51}-\frac{4154140621425}{128}\cdot t^{49}+\frac{2814095259675}{128}\cdot t^{47}-\frac{3324630574545}{256}\cdot t^{45}+\frac{109712808959985}{16384}\cdot t^{43}-\frac{98774343460485}{32768}\cdot t^{41}+\frac{77581380878925}{65536}\cdot t^{39}-\frac{53081997443475}{131072}\cdot t^{37}+\frac{505037289962205}{4194304}\cdot t^{35}-\frac{260170725132045}{8388608}\cdot t^{33}+\frac{28907858348005}{4194304}\cdot t^{31}-\frac{11027197811175}{8388608}\cdot t^{29}+\frac{57397978350475}{268435456}\cdot t^{27}-\frac{15801325804719}{536870912}\cdot t^{25}+\frac{3646459801089}{1073741824}\cdot t^{23}-\frac{697319977079}{2147483648}\cdot t^{21}+\frac{3486599885395}{137438953472}\cdot t^{19}-\frac{437423756715}{274877906944}\cdot t^{17}+\frac{21554214099}{274877906944}\cdot t^{15}-\frac{1622360201}{549755813888}\cdot t^{13}+\frac{5752004349}{70368744177664}\cdot t^{11}-\frac{222945905}{140737488355328}\cdot t^9+\frac{5620485}{281474976710656}\cdot t^7-\frac{82251}{562949953421312}\cdot t^5+\frac{9139}{18014398509481984}\cdot t^3-\frac{19}{36028797018963968}\cdot t$

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.