Rule: Q[8, 27, 72]

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.

• $P_1$:
  $256\cdot t^8-448\cdot t^6+240\cdot t^4-40\cdot t^2+1$
• $P_2$:
  $256\cdot t^{35}-2176\cdot t^{33}+8448\cdot t^{31}-19840\cdot t^{29}+31465\cdot t^{27}-\frac{71253}{2}\cdot t^{25}+\frac{118755}{4}\cdot t^{23}-\frac{148005}{8}\cdot t^{21}+\frac{2220075}{256}\cdot t^{19}-\frac{1562275}{512}\cdot t^{17}+\frac{408595}{512}\cdot t^{15}-\frac{156009}{1024}\cdot t^{13}+\frac{676039}{32768}\cdot t^{11}-\frac{124355}{65536}\cdot t^9+\frac{14535}{131072}\cdot t^7-\frac{969}{262144}\cdot t^5+\frac{969}{16777216}\cdot t^3-\frac{9}{33554432}\cdot t$
• $P_3$:
  $256\cdot t^{107}-6784\cdot t^{105}+87360\cdot t^{103}-728416\cdot t^{101}+4421275\cdot t^{99}-\frac{41645835}{2}\cdot t^{97}+79208745\cdot t^{95}-\frac{500236275}{2}\cdot t^{93}+\frac{42800215689}{64}\cdot t^{91}-\frac{196708062005}{128}\cdot t^{89}+\frac{786029357971}{256}\cdot t^{87}-\frac{2755891122933}{512}\cdot t^{85}+\frac{546585072715045}{65536}\cdot t^{83}-\frac{1506096358258541}{131072}\cdot t^{81}+\frac{1854009194816745}{131072}\cdot t^{79}-\frac{4094768694788811}{262144}\cdot t^{77}+\frac{260462895672870891}{16777216}\cdot t^{75}-\frac{467216894306539575}{33554432}\cdot t^{73}+\frac{757929628541719755}{67108864}\cdot t^{71}-\frac{1113811429288097925}{134217728}\cdot t^{69}+\frac{23754560119180706655}{4294967296}\cdot t^{67}-\frac{28747308387251528415}{8589934592}\cdot t^{65}+\frac{3950475782603275575}{2147483648}\cdot t^{63}-\frac{3946434375153042045}{4294967296}\cdot t^{61}+\frac{57317261162937039225}{137438953472}\cdot t^{59}-\frac{47262570530016999573}{274877906944}\cdot t^{57}+\frac{35380423342357941519}{549755813888}\cdot t^{55}-\frac{24023744244810947945}{1099511627776}\cdot t^{53}+\frac{472924565276421232403}{70368744177664}\cdot t^{51}-\frac{263194596563700162075}{140737488355328}\cdot t^{49}+\frac{66136078110878502265}{140737488355328}\cdot t^{47}-\frac{29951026576397009195}{281474976710656}\cdot t^{45}+\frac{780303060806132607975}{36028797018963968}\cdot t^{43}-\frac{284692389457752624243}{72057594037927936}\cdot t^{41}+\frac{92785277963178518235}{144115188075855872}\cdot t^{39}-\frac{26909546368186020357}{288230376151711744}\cdot t^{37}+\frac{110628135069209194801}{9223372036854775808}\cdot t^{35}-\frac{25056619857700597985}{18446744073709551616}\cdot t^{33}+\frac{1243411210983638697}{9223372036854775808}\cdot t^{31}-\frac{214859239356147155}{18446744073709551616}\cdot t^{29}+\frac{513134418697622029}{590295810358705651712}\cdot t^{27}-\frac{65566137955174857}{1180591620717411303424}\cdot t^{25}+\frac{7095902376101175}{2361183241434822606848}\cdot t^{23}-\frac{642312451217745}{4722366482869645213696}\cdot t^{21}+\frac{6131164307078475}{1208925819614629174706176}\cdot t^{19}-\frac{369816259792035}{2417851639229258349412352}\cdot t^{17}+\frac{8817498480315}{2417851639229258349412352}\cdot t^{15}-\frac{322928964225}{4835703278458516698824704}\cdot t^{13}+\frac{279871768995}{309485009821345068724781056}\cdot t^{11}-\frac{5324436975}{618970019642690137449562112}\cdot t^9+\frac{66096459}{1237940039285380274899124224}\cdot t^7-\frac{477477}{2475880078570760549798248448}\cdot t^5+\frac{26235}{79228162514264337593543950336}\cdot t^3-\frac{27}{158456325028528675187087900672}\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.