Rule: Q[2, 3, 24, 30, 60]

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.

• $P_1$:
  $4\cdot t^2-1$
• $P_2$:
  $4\cdot t^5-4\cdot t^3+\frac{3}{4}\cdot t$
• $P_3$:
  $4\cdot t^{29}-28\cdot t^{27}+\frac{351}{4}\cdot t^{25}-\frac{325}{2}\cdot t^{23}+\frac{6325}{32}\cdot t^{21}-\frac{5313}{32}\cdot t^{19}+\frac{100947}{1024}\cdot t^{17}-\frac{10659}{256}\cdot t^{15}+\frac{101745}{8192}\cdot t^{13}-\frac{20995}{8192}\cdot t^{11}+\frac{46189}{131072}\cdot t^9-\frac{1989}{65536}\cdot t^7+\frac{1547}{1048576}\cdot t^5-\frac{35}{1048576}\cdot t^3+\frac{15}{67108864}\cdot t$
• $P_4$:
  $4\cdot t^{59}-58\cdot t^{57}+399\cdot t^{55}-\frac{3465}{2}\cdot t^{53}+\frac{341055}{64}\cdot t^{51}-\frac{1581255}{128}\cdot t^{49}+\frac{2869685}{128}\cdot t^{47}-\frac{8361535}{256}\cdot t^{45}+\frac{318381525}{8192}\cdot t^{43}-\frac{626358425}{16384}\cdot t^{41}+\frac{1027227817}{32768}\cdot t^{39}-\frac{1412200023}{65536}\cdot t^{37}+\frac{52251400851}{4194304}\cdot t^{35}-\frac{50883115395}{8388608}\cdot t^{33}+\frac{10429458435}{4194304}\cdot t^{31}-\frac{7184738033}{8388608}\cdot t^{29}+\frac{132591074609}{536870912}\cdot t^{27}-\frac{63665481789}{1073741824}\cdot t^{25}+\frac{25264080075}{2147483648}\cdot t^{23}-\frac{8205150525}{4294967296}\cdot t^{21}+\frac{34461632205}{137438953472}\cdot t^{19}-\frac{7195285845}{274877906944}\cdot t^{17}+\frac{585262485}{274877906944}\cdot t^{15}-\frac{72212175}{549755813888}\cdot t^{13}+\frac{104306475}{17592186044416}\cdot t^{11}-\frac{6556407}{35184372088832}\cdot t^9+\frac{267003}{70368744177664}\cdot t^7-\frac{6293}{140737488355328}\cdot t^5+\frac{4495}{18014398509481984}\cdot t^3-\frac{15}{36028797018963968}\cdot t$
• $P_5$:
  $4\cdot t^{119}-118\cdot t^{117}+\frac{3393}{2}\cdot t^{115}-\frac{63365}{4}\cdot t^{113}+\frac{1728335}{16}\cdot t^{111}-\frac{18350409}{32}\cdot t^{109}+\frac{315820197}{128}\cdot t^{107}-\frac{2264243157}{256}\cdot t^{105}+\frac{441527415615}{16384}\cdot t^{103}-\frac{2321665179405}{32768}\cdot t^{101}+\frac{21317107556355}{131072}\cdot t^{99}-\frac{86246279195895}{262144}\cdot t^{97}+\frac{309847743777845}{524288}\cdot t^{95}-\frac{994586754829675}{1048576}\cdot t^{93}+\frac{5734288594557075}{4194304}\cdot t^{91}-\frac{14909150345848395}{8388608}\cdot t^{89}+\frac{1122773706814275285}{536870912}\cdot t^{87}-\frac{2398798650595204935}{1073741824}\cdot t^{85}+\frac{9328661418981352525}{4294967296}\cdot t^{83}-\frac{16542696617401533425}{8589934592}\cdot t^{81}+\frac{53598337040380968297}{34359738368}\cdot t^{79}-\frac{79430724589424609583}{68719476736}\cdot t^{77}+\frac{215597681028438226011}{274877906944}\cdot t^{75}-\frac{268168339244247457275}{549755813888}\cdot t^{73}+\frac{19576288764830064381075}{70368744177664}\cdot t^{71}-\frac{20482980033937983152409}{140737488355328}\cdot t^{69}+\frac{39323298821291741796687}{562949953421312}\cdot t^{67}-\frac{34625174708831557591587}{1125899906842624}\cdot t^{65}+\frac{13979107801702181636355}{1125899906842624}\cdot t^{63}-\frac{10345281370490473943085}{2251799813685248}\cdot t^{61}+\frac{14023603635553753567293}{9007199254740992}\cdot t^{59}-\frac{8696769054161823977397}{18014398509481984}\cdot t^{57}+\frac{315455532055506160634673}{2305843009213693952}\cdot t^{55}-\frac{163166654511468703776555}{4611686018427387904}\cdot t^{53}+\frac{153791826208484181808545}{18446744073709551616}\cdot t^{51}-\frac{65910782660778935060805}{36893488147419103232}\cdot t^{49}+\frac{51263942069494727269515}{147573952589676412928}\cdot t^{47}-\frac{18045041151782416209165}{295147905179352825856}\cdot t^{45}+\frac{11466361194008082186825}{1180591620717411303424}\cdot t^{43}-\frac{3277658802845615136025}{2361183241434822606848}\cdot t^{41}+\frac{26876802183334044115405}{151115727451828646838272}\cdot t^{39}-\frac{6148721956730634976695}{302231454903657293676544}\cdot t^{37}+\frac{2500029806582785649865}{1208925819614629174706176}\cdot t^{35}-\frac{449265398645955137925}{2417851639229258349412352}\cdot t^{33}+\frac{70936641891466600725}{4835703278458516698824704}\cdot t^{31}-\frac{9773492882824287211}{9671406556917033397649408}\cdot t^{29}+\frac{2331397244669013283}{38685626227668133590597632}\cdot t^{27}-\frac{238507849862670843}{77371252455336267181195264}\cdot t^{25}+\frac{662521805174085675}{4951760157141521099596496896}\cdot t^{23}-\frac{48179941566267225}{9903520314283042199192993792}\cdot t^{21}+\frac{5781592987952067}{39614081257132168796771975168}\cdot t^{19}-\frac{280946973839103}{79228162514264337593543950336}\cdot t^{17}+\frac{21611305679931}{316912650057057350374175801344}\cdot t^{15}-\frac{639027625005}{633825300114114700748351602688}\cdot t^{13}+\frac{27970906145}{2535301200456458802993406410752}\cdot t^{11}-\frac{430321633}{5070602400912917605986812821504}\cdot t^9+\frac{553270671}{1298074214633706907132624082305024}\cdot t^7-\frac{3235501}{2596148429267413814265248164610048}\cdot t^5+\frac{17995}{10384593717069655257060992658440192}\cdot t^3-\frac{15}{20769187434139310514121985316880384}\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.