Rule: Q[4, 90]

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.

• $P_1$:
  $16\cdot t^4-12\cdot t^2+1$
• $P_2$:
  $16\cdot t^{94}-372\cdot t^{92}+4186\cdot t^{90}-\frac{121485}{4}\cdot t^{88}+\frac{1277595}{8}\cdot t^{86}-\frac{20753821}{32}\cdot t^{84}+\frac{135482809}{64}\cdot t^{82}-\frac{5843355957}{1024}\cdot t^{80}+\frac{26530179345}{2048}\cdot t^{78}-\frac{205865965305}{8192}\cdot t^{76}+\frac{690256471905}{16384}\cdot t^{74}-\frac{8070920911755}{131072}\cdot t^{72}+\frac{20712122339805}{262144}\cdot t^{70}-\frac{93845732552775}{1048576}\cdot t^{68}+\frac{188519028884675}{2097152}\cdot t^{66}-\frac{5391644226101705}{67108864}\cdot t^{64}+\frac{4299665648663385}{67108864}\cdot t^{62}-\frac{12263450590682445}{268435456}\cdot t^{60}+\frac{15661116555200525}{536870912}\cdot t^{58}-\frac{71711428436970825}{4294967296}\cdot t^{56}+\frac{73623733195290047}{8589934592}\cdot t^{54}-\frac{135592744147310241}{34359738368}\cdot t^{52}+\frac{111952664221253661}{68719476736}\cdot t^{50}-\frac{662521805174085675}{1099511627776}\cdot t^{48}+\frac{438570772439183475}{2199023255552}\cdot t^{46}-\frac{518766570828062739}{8796093022208}\cdot t^{44}+\frac{273552494985143451}{17592186044416}\cdot t^{42}-\frac{513134418697622029}{140737488355328}\cdot t^{40}+\frac{213350131441441995}{281474976710656}\cdot t^{38}-\frac{156724286732846105}{1125899906842624}\cdot t^{36}+\frac{50634000329073357}{2251799813685248}\cdot t^{34}-\frac{916312070471295267}{288230376151711744}\cdot t^{32}+\frac{450883717216034179}{1152921504606846976}\cdot t^{30}-\frac{191724747789809255}{4611686018427387904}\cdot t^{28}+\frac{34943083251951735}{9223372036854775808}\cdot t^{26}-\frac{21631432489303455}{73786976294838206464}\cdot t^{24}+\frac{2810864108779545}{147573952589676412928}\cdot t^{22}-\frac{605134770855615}{590295810358705651712}\cdot t^{20}+\frac{53081997443475}{1180591620717411303424}\cdot t^{18}-\frac{29749251314475}{18889465931478580854784}\cdot t^{16}+\frac{1622686435335}{37778931862957161709568}\cdot t^{14}-\frac{133391567855}{151115727451828646838272}\cdot t^{12}+\frac{3955006055}{302231454903657293676544}\cdot t^{10}-\frac{318381525}{2417851639229258349412352}\cdot t^8+\frac{3972675}{4835703278458516698824704}\cdot t^6-\frac{52969}{19342813113834066795298816}\cdot t^4+\frac{141}{38685626227668133590597632}\cdot t^2-\frac{1}{1237940039285380274899124224}$

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.