Rule: Q[26, 54]

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.

• $P_1$:
  $67108864\cdot t^{26}-419430400\cdot t^{24}+1157627904\cdot t^{22}-1857028096\cdot t^{20}+1917583360\cdot t^{18}-1333592064\cdot t^{16}+635043840\cdot t^{14}-206389248\cdot t^{12}+44808192\cdot t^{10}-6223360\cdot t^8+512512\cdot t^6-21840\cdot t^4+364\cdot t^2-1$
• $P_2$:
  $67108864\cdot t^{80}-1325400064\cdot t^{78}+12595494912\cdot t^{76}-76703334400\cdot t^{74}+336324198400\cdot t^{72}-1131111383040\cdot t^{70}+3035148877824\cdot t^{68}-6673811914752\cdot t^{66}+12256272737280\cdot t^{64}-19065313146880\cdot t^{62}+25389089549824\cdot t^{60}-29180966560512\cdot t^{58}+29128102490656\cdot t^{56}-25371763481680\cdot t^{54}+19353408071580\cdot t^{52}-12960918738846\cdot t^{50}+\frac{122131734269895}{16}\cdot t^{48}-\frac{1012974972473835}{256}\cdot t^{46}+\frac{1849081298960175}{1024}\cdot t^{44}-\frac{1484915881847475}{2048}\cdot t^{42}+\frac{4191844505805495}{16384}\cdot t^{40}-\frac{2594951360736735}{32768}\cdot t^{38}+\frac{2810864108779545}{131072}\cdot t^{36}-\frac{1327469556620025}{262144}\cdot t^{34}+\frac{4355031703297275}{4194304}\cdot t^{32}-\frac{771462758869803}{4194304}\cdot t^{30}+\frac{469351468683027}{16777216}\cdot t^{28}-\frac{121683714103007}{33554432}\cdot t^{26}+\frac{106596245508025}{268435456}\cdot t^{24}-\frac{19509657665925}{536870912}\cdot t^{22}+\frac{5891151530495}{2147483648}\cdot t^{20}-\frac{722141155351}{4294967296}\cdot t^{18}+\frac{2254848913647}{274877906944}\cdot t^{16}-\frac{341643774795}{1099511627776}\cdot t^{14}+\frac{38910617655}{4398046511104}\cdot t^{12}-\frac{1595093643}{8796093022208}\cdot t^{10}+\frac{177232627}{70368744177664}\cdot t^8-\frac{3048227}{140737488355328}\cdot t^6+\frac{55965}{562949953421312}\cdot t^4-\frac{205}{1125899906842624}\cdot t^2+\frac{1}{18014398509481984}$

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.