Rule: Q[2, 3, 18, 24, 48]

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.

• $P_1$:
  $4\cdot t^2-1$
• $P_2$:
  $4\cdot t^5-4\cdot t^3+\frac{3}{4}\cdot t$
• $P_3$:
  $4\cdot t^{23}-22\cdot t^{21}+\frac{105}{2}\cdot t^{19}-\frac{285}{4}\cdot t^{17}+\frac{969}{16}\cdot t^{15}-\frac{1071}{32}\cdot t^{13}+\frac{1547}{128}\cdot t^{11}-\frac{715}{256}\cdot t^9+\frac{6435}{16384}\cdot t^7-\frac{1001}{32768}\cdot t^5+\frac{143}{131072}\cdot t^3-\frac{3}{262144}\cdot t$
• $P_4$:
  $4\cdot t^{47}-46\cdot t^{45}+\frac{495}{2}\cdot t^{43}-\frac{3311}{4}\cdot t^{41}+\frac{61705}{32}\cdot t^{39}-\frac{212667}{64}\cdot t^{37}+\frac{1124097}{256}\cdot t^{35}-\frac{2330445}{512}\cdot t^{33}+\frac{15380937}{4096}\cdot t^{31}-\frac{20376455}{8192}\cdot t^{29}+\frac{43541267}{32768}\cdot t^{27}-\frac{37550331}{65536}\cdot t^{25}+\frac{104306475}{524288}\cdot t^{23}-\frac{57998985}{1048576}\cdot t^{21}+\frac{51175575}{4194304}\cdot t^{19}-\frac{17678835}{8388608}\cdot t^{17}+\frac{300540195}{1073741824}\cdot t^{15}-\frac{59879925}{2147483648}\cdot t^{13}+\frac{17298645}{8589934592}\cdot t^{11}-\frac{1726725}{17179869184}\cdot t^9+\frac{444015}{137438953472}\cdot t^7-\frac{16445}{274877906944}\cdot t^5+\frac{575}{1099511627776}\cdot t^3-\frac{3}{2199023255552}\cdot t$
• $P_5$:
  $4\cdot t^{95}-94\cdot t^{93}+\frac{2139}{2}\cdot t^{91}-\frac{31395}{4}\cdot t^{89}+\frac{1336335}{32}\cdot t^{87}-\frac{10987317}{64}\cdot t^{85}+\frac{145276747}{256}\cdot t^{83}-\frac{793542167}{512}\cdot t^{81}+\frac{29216779785}{8192}\cdot t^{79}-\frac{114964110495}{16384}\cdot t^{77}+\frac{782290668159}{65536}\cdot t^{75}-\frac{2321771769135}{131072}\cdot t^{73}+\frac{24212762735265}{1048576}\cdot t^{71}-\frac{55763406299475}{2097152}\cdot t^{69}+\frac{227911064771025}{8388608}\cdot t^{67}-\frac{414741863546285}{16777216}\cdot t^{65}+\frac{5391644226101705}{268435456}\cdot t^{63}-\frac{7840566771092055}{536870912}\cdot t^{61}+\frac{20439084317804075}{2147483648}\cdot t^{59}-\frac{23903809478990275}{4294967296}\cdot t^{57}+\frac{100395999811759155}{34359738368}\cdot t^{55}-\frac{94659085536801489}{68719476736}\cdot t^{53}+\frac{160245970355912103}{274877906944}\cdot t^{51}-\frac{121687678501362675}{549755813888}\cdot t^{49}+\frac{662521805174085675}{8796093022208}\cdot t^{47}-\frac{403485110644048797}{17592186044416}\cdot t^{45}+\frac{438956329162206933}{70368744177664}\cdot t^{43}-\frac{212763051655111573}{140737488355328}\cdot t^{41}+\frac{366524584784015735}{1125899906842624}\cdot t^{39}-\frac{139781120599565445}{2251799813685248}\cdot t^{37}+\frac{94034572039707663}{9007199254740992}\cdot t^{35}-\frac{27767032438524099}{18014398509481984}\cdot t^{33}+\frac{916312070471295267}{4611686018427387904}\cdot t^{31}-\frac{204947144189106445}{9223372036854775808}\cdot t^{29}+\frac{78945484384039105}{36893488147419103232}\cdot t^{27}-\frac{12978859493582073}{73786976294838206464}\cdot t^{25}+\frac{7210477496434485}{590295810358705651712}\cdot t^{23}-\frac{835662302610135}{1180591620717411303424}\cdot t^{21}+\frac{159245992330425}{4722366482869645213696}\cdot t^{19}-\frac{12249691717725}{9444732965739290427392}\cdot t^{17}+\frac{5949850262895}{151115727451828646838272}\cdot t^{15}-\frac{277044025545}{302231454903657293676544}\cdot t^{13}+\frac{19055938265}{1208925819614629174706176}\cdot t^{11}-\frac{459884425}{2417851639229258349412352}\cdot t^9+\frac{28943775}{19342813113834066795298816}\cdot t^7-\frac{264845}{38685626227668133590597632}\cdot t^5+\frac{2303}{154742504910672534362390528}\cdot t^3-\frac{3}{309485009821345068724781056}\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.