Rule: Q[1, 8, 30, 80]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^9-4\cdot t^7+\frac{21}{8}\cdot t^5-\frac{5}{8}\cdot t^3+\frac{5}{128}\cdot t$
• $P_3$:
  $2\cdot t^{39}-19\cdot t^{37}+\frac{333}{4}\cdot t^{35}-\frac{1785}{8}\cdot t^{33}+\frac{6545}{16}\cdot t^{31}-\frac{17391}{32}\cdot t^{29}+\frac{69223}{128}\cdot t^{27}-\frac{105183}{256}\cdot t^{25}+\frac{7888725}{32768}\cdot t^{23}-\frac{7153575}{65536}\cdot t^{21}+\frac{10015005}{262144}\cdot t^{19}-\frac{5368545}{524288}\cdot t^{17}+\frac{4345965}{2097152}\cdot t^{15}-\frac{1300075}{4194304}\cdot t^{13}+\frac{557175}{16777216}\cdot t^{11}-\frac{81719}{33554432}\cdot t^9+\frac{245157}{2147483648}\cdot t^7-\frac{13167}{4294967296}\cdot t^5+\frac{665}{17179869184}\cdot t^3-\frac{5}{34359738368}\cdot t$
• $P_4$:
  $2\cdot t^{119}-59\cdot t^{117}+\frac{3393}{4}\cdot t^{115}-\frac{63365}{8}\cdot t^{113}+\frac{1728335}{32}\cdot t^{111}-\frac{18350409}{64}\cdot t^{109}+\frac{315820197}{256}\cdot t^{107}-\frac{2264243157}{512}\cdot t^{105}+\frac{441527415615}{32768}\cdot t^{103}-\frac{2321665179405}{65536}\cdot t^{101}+\frac{21317107556355}{262144}\cdot t^{99}-\frac{86246279195895}{524288}\cdot t^{97}+\frac{309847743777845}{1048576}\cdot t^{95}-\frac{994586754829675}{2097152}\cdot t^{93}+\frac{5734288594557075}{8388608}\cdot t^{91}-\frac{14909150345848395}{16777216}\cdot t^{89}+\frac{1122773706814275285}{1073741824}\cdot t^{87}-\frac{2398798650595204935}{2147483648}\cdot t^{85}+\frac{9328661418981352525}{8589934592}\cdot t^{83}-\frac{16542696617401533425}{17179869184}\cdot t^{81}+\frac{53598337040380968297}{68719476736}\cdot t^{79}-\frac{79430724589424609583}{137438953472}\cdot t^{77}+\frac{215597681028438226011}{549755813888}\cdot t^{75}-\frac{268168339244247457275}{1099511627776}\cdot t^{73}+\frac{19576288764830064381075}{140737488355328}\cdot t^{71}-\frac{20482980033937983152409}{281474976710656}\cdot t^{69}+\frac{39323298821291741796687}{1125899906842624}\cdot t^{67}-\frac{34625174708831557591587}{2251799813685248}\cdot t^{65}+\frac{13979107801702181636355}{2251799813685248}\cdot t^{63}-\frac{10345281370490473943085}{4503599627370496}\cdot t^{61}+\frac{14023603635553753567293}{18014398509481984}\cdot t^{59}-\frac{8696769054161823977397}{36028797018963968}\cdot t^{57}+\frac{315455532055506160634673}{4611686018427387904}\cdot t^{55}-\frac{163166654511468703776555}{9223372036854775808}\cdot t^{53}+\frac{153791826208484181808545}{36893488147419103232}\cdot t^{51}-\frac{65910782660778935060805}{73786976294838206464}\cdot t^{49}+\frac{51263942069494727269515}{295147905179352825856}\cdot t^{47}-\frac{18045041151782416209165}{590295810358705651712}\cdot t^{45}+\frac{11466361194008082186825}{2361183241434822606848}\cdot t^{43}-\frac{3277658802845615136025}{4722366482869645213696}\cdot t^{41}+\frac{26876802183334044115405}{302231454903657293676544}\cdot t^{39}-\frac{6148721956730634976695}{604462909807314587353088}\cdot t^{37}+\frac{2500029806582785649865}{2417851639229258349412352}\cdot t^{35}-\frac{449265398645955137925}{4835703278458516698824704}\cdot t^{33}+\frac{70936641891466600725}{9671406556917033397649408}\cdot t^{31}-\frac{9773492882824287211}{19342813113834066795298816}\cdot t^{29}+\frac{2331397244669013283}{77371252455336267181195264}\cdot t^{27}-\frac{238507849862670843}{154742504910672534362390528}\cdot t^{25}+\frac{662521805174085675}{9903520314283042199192993792}\cdot t^{23}-\frac{48179941566267225}{19807040628566084398385987584}\cdot t^{21}+\frac{5781592987952067}{79228162514264337593543950336}\cdot t^{19}-\frac{280946973839103}{158456325028528675187087900672}\cdot t^{17}+\frac{21611305679931}{633825300114114700748351602688}\cdot t^{15}-\frac{639027625005}{1267650600228229401496703205376}\cdot t^{13}+\frac{27970906145}{5070602400912917605986812821504}\cdot t^{11}-\frac{430321633}{10141204801825835211973625643008}\cdot t^9+\frac{553270671}{2596148429267413814265248164610048}\cdot t^7-\frac{3235501}{5192296858534827628530496329220096}\cdot t^5+\frac{17995}{20769187434139310514121985316880384}\cdot t^3-\frac{15}{41538374868278621028243970633760768}\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.