Rule: Q[2, 6, 18, 27, 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.

• $P_1$:
  $4\cdot t^2-1$
• $P_2$:
  $4\cdot t^8-7\cdot t^6+\frac{15}{4}\cdot t^4-\frac{5}{8}\cdot t^2+\frac{1}{64}$
• $P_3$:
  $4\cdot t^{26}-25\cdot t^{24}+69\cdot t^{22}-\frac{1771}{16}\cdot t^{20}+\frac{7315}{64}\cdot t^{18}-\frac{20349}{256}\cdot t^{16}+\frac{4845}{128}\cdot t^{14}-\frac{12597}{1024}\cdot t^{12}+\frac{21879}{8192}\cdot t^{10}-\frac{12155}{32768}\cdot t^8+\frac{1001}{32768}\cdot t^6-\frac{1365}{1048576}\cdot t^4+\frac{91}{4194304}\cdot t^2-\frac{1}{16777216}$
• $P_4$:
  $4\cdot t^{53}-52\cdot t^{51}+\frac{1275}{4}\cdot t^{49}-1225\cdot t^{47}+\frac{52969}{16}\cdot t^{45}-\frac{107019}{16}\cdot t^{43}+\frac{10737573}{1024}\cdot t^{41}-\frac{6690585}{512}\cdot t^{39}+\frac{215553195}{16384}\cdot t^{37}-\frac{177232627}{16384}\cdot t^{35}+\frac{1917334783}{262144}\cdot t^{33}-\frac{133767543}{32768}\cdot t^{31}+\frac{987331865}{524288}\cdot t^{29}-\frac{376038215}{524288}\cdot t^{27}+\frac{3771126099}{16777216}\cdot t^{25}-\frac{483477705}{8388608}\cdot t^{23}+\frac{6437887335}{536870912}\cdot t^{21}-\frac{1074687075}{536870912}\cdot t^{19}+\frac{2268783825}{8589934592}\cdot t^{17}-\frac{57998985}{2147483648}\cdot t^{15}+\frac{71645805}{34359738368}\cdot t^{13}-\frac{4032015}{34359738368}\cdot t^{11}+\frac{20160075}{4398046511104}\cdot t^9-\frac{254475}{2199023255552}\cdot t^7+\frac{118755}{70368744177664}\cdot t^5-\frac{819}{70368744177664}\cdot t^3+\frac{27}{1125899906842624}\cdot t$
• $P_5$:
  $4\cdot t^{107}-106\cdot t^{105}+1365\cdot t^{103}-\frac{22763}{2}\cdot t^{101}+\frac{4421275}{64}\cdot t^{99}-\frac{41645835}{128}\cdot t^{97}+\frac{79208745}{64}\cdot t^{95}-\frac{500236275}{128}\cdot t^{93}+\frac{42800215689}{4096}\cdot t^{91}-\frac{196708062005}{8192}\cdot t^{89}+\frac{786029357971}{16384}\cdot t^{87}-\frac{2755891122933}{32768}\cdot t^{85}+\frac{546585072715045}{4194304}\cdot t^{83}-\frac{1506096358258541}{8388608}\cdot t^{81}+\frac{1854009194816745}{8388608}\cdot t^{79}-\frac{4094768694788811}{16777216}\cdot t^{77}+\frac{260462895672870891}{1073741824}\cdot t^{75}-\frac{467216894306539575}{2147483648}\cdot t^{73}+\frac{757929628541719755}{4294967296}\cdot t^{71}-\frac{1113811429288097925}{8589934592}\cdot t^{69}+\frac{23754560119180706655}{274877906944}\cdot t^{67}-\frac{28747308387251528415}{549755813888}\cdot t^{65}+\frac{3950475782603275575}{137438953472}\cdot t^{63}-\frac{3946434375153042045}{274877906944}\cdot t^{61}+\frac{57317261162937039225}{8796093022208}\cdot t^{59}-\frac{47262570530016999573}{17592186044416}\cdot t^{57}+\frac{35380423342357941519}{35184372088832}\cdot t^{55}-\frac{24023744244810947945}{70368744177664}\cdot t^{53}+\frac{472924565276421232403}{4503599627370496}\cdot t^{51}-\frac{263194596563700162075}{9007199254740992}\cdot t^{49}+\frac{66136078110878502265}{9007199254740992}\cdot t^{47}-\frac{29951026576397009195}{18014398509481984}\cdot t^{45}+\frac{780303060806132607975}{2305843009213693952}\cdot t^{43}-\frac{284692389457752624243}{4611686018427387904}\cdot t^{41}+\frac{92785277963178518235}{9223372036854775808}\cdot t^{39}-\frac{26909546368186020357}{18446744073709551616}\cdot t^{37}+\frac{110628135069209194801}{590295810358705651712}\cdot t^{35}-\frac{25056619857700597985}{1180591620717411303424}\cdot t^{33}+\frac{1243411210983638697}{590295810358705651712}\cdot t^{31}-\frac{214859239356147155}{1180591620717411303424}\cdot t^{29}+\frac{513134418697622029}{37778931862957161709568}\cdot t^{27}-\frac{65566137955174857}{75557863725914323419136}\cdot t^{25}+\frac{7095902376101175}{151115727451828646838272}\cdot t^{23}-\frac{642312451217745}{302231454903657293676544}\cdot t^{21}+\frac{6131164307078475}{77371252455336267181195264}\cdot t^{19}-\frac{369816259792035}{154742504910672534362390528}\cdot t^{17}+\frac{8817498480315}{154742504910672534362390528}\cdot t^{15}-\frac{322928964225}{309485009821345068724781056}\cdot t^{13}+\frac{279871768995}{19807040628566084398385987584}\cdot t^{11}-\frac{5324436975}{39614081257132168796771975168}\cdot t^9+\frac{66096459}{79228162514264337593543950336}\cdot t^7-\frac{477477}{158456325028528675187087900672}\cdot t^5+\frac{26235}{5070602400912917605986812821504}\cdot t^3-\frac{27}{10141204801825835211973625643008}\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.