Rule: Q[28, 58]

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.

• $P_1$:
  $268435456\cdot t^{28}-1811939328\cdot t^{26}+5452595200\cdot t^{24}-9646899200\cdot t^{22}+11142168576\cdot t^{20}-8820883456\cdot t^{18}+4889837568\cdot t^{16}-1905131520\cdot t^{14}+515973120\cdot t^{12}-94595072\cdot t^{10}+11202048\cdot t^8-792064\cdot t^6+29120\cdot t^4-420\cdot t^2+1$
• $P_2$:
  $268435456\cdot t^{86}-5704253440\cdot t^{84}+58485374976\cdot t^{82}-385376845824\cdot t^{80}+1834022338560\cdot t^{78}-6716547661824\cdot t^{76}+19693581107200\cdot t^{74}-47493180866560\cdot t^{72}+96038425866240\cdot t^{70}-165194300902400\cdot t^{68}+244358842503680\cdot t^{66}-313486672948800\cdot t^{64}+351105073702656\cdot t^{62}-345083001232704\cdot t^{60}+298824321028320\cdot t^{58}-228683612342506\cdot t^{56}+\frac{620022470083555}{4}\cdot t^{54}-\frac{1491180091915239}{16}\cdot t^{52}+\frac{1592032851754917}{32}\cdot t^{50}-\frac{6037895490401775}{256}\cdot t^{48}+\frac{2541323176557165}{256}\cdot t^{46}-\frac{3795482666286675}{1024}\cdot t^{44}+\frac{2510857763851185}{2048}\cdot t^{42}-\frac{93993414551124795}{262144}\cdot t^{40}+\frac{96977332473382725}{1048576}\cdot t^{38}-\frac{87967825456500717}{4194304}\cdot t^{36}+\frac{34943083251951735}{8388608}\cdot t^{34}-\frac{48402641245296107}{67108864}\cdot t^{32}+\frac{3633128035361209}{33554432}\cdot t^{30}-\frac{1879204156221315}{134217728}\cdot t^{28}+\frac{415403024006817}{268435456}\cdot t^{26}-\frac{622147386185325}{4294967296}\cdot t^{24}+\frac{780512175396135}{68719476736}\cdot t^{22}-\frac{202355008436035}{274877906944}\cdot t^{20}+\frac{21335988680825}{549755813888}\cdot t^{18}-\frac{7174519270695}{4398046511104}\cdot t^{16}+\frac{234461414075}{4398046511104}\cdot t^{14}-\frac{23065933709}{17592186044416}\cdot t^{12}+\frac{817589487}{35184372088832}\cdot t^{10}-\frac{314457495}{1125899906842624}\cdot t^8+\frac{9366819}{4503599627370496}\cdot t^6-\frac{148995}{18014398509481984}\cdot t^4+\frac{473}{36028797018963968}\cdot t^2-\frac{1}{288230376151711744}$

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.