Rule: Q[1, 20, 22, 88]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{21}-10\cdot t^{19}+\frac{171}{8}\cdot t^{17}-\frac{51}{2}\cdot t^{15}+\frac{595}{32}\cdot t^{13}-\frac{273}{32}\cdot t^{11}+\frac{5005}{2048}\cdot t^9-\frac{429}{1024}\cdot t^7+\frac{1287}{32768}\cdot t^5-\frac{55}{32768}\cdot t^3+\frac{11}{524288}\cdot t$
• $P_3$:
  $2\cdot t^{43}-21\cdot t^{41}+\frac{205}{2}\cdot t^{39}-\frac{1235}{4}\cdot t^{37}+\frac{82251}{128}\cdot t^{35}-\frac{250971}{256}\cdot t^{33}+\frac{145299}{128}\cdot t^{31}-\frac{260865}{256}\cdot t^{29}+\frac{5883955}{8192}\cdot t^{27}-\frac{6556407}{16384}\cdot t^{25}+\frac{5785065}{32768}\cdot t^{23}-\frac{4032015}{65536}\cdot t^{21}+\frac{141120525}{8388608}\cdot t^{19}-\frac{59879925}{16777216}\cdot t^{17}+\frac{9694845}{16777216}\cdot t^{15}-\frac{2340135}{33554432}\cdot t^{13}+\frac{13037895}{2147483648}\cdot t^{11}-\frac{1562275}{4294967296}\cdot t^9+\frac{120175}{8589934592}\cdot t^7-\frac{5313}{17179869184}\cdot t^5+\frac{1771}{549755813888}\cdot t^3-\frac{11}{1099511627776}\cdot t$
• $P_4$:
  $2\cdot t^{131}-65\cdot t^{129}+1032\cdot t^{127}-10668\cdot t^{125}+\frac{10334625}{128}\cdot t^{123}-\frac{122111325}{256}\cdot t^{121}+\frac{1172656375}{512}\cdot t^{119}-\frac{9409394753}{1024}\cdot t^{117}+\frac{1029873432159}{32768}\cdot t^{115}-\frac{6098302030535}{65536}\cdot t^{113}+\frac{15815596413617}{65536}\cdot t^{111}-\frac{72542611649235}{131072}\cdot t^{109}+\frac{4744286801859969}{4194304}\cdot t^{107}-\frac{17391629252325717}{8388608}\cdot t^{105}+\frac{57480808545822285}{16777216}\cdot t^{103}-\frac{172049394467922771}{33554432}\cdot t^{101}+\frac{14980162794189827475}{2147483648}\cdot t^{99}-\frac{37170726196733940195}{4294967296}\cdot t^{97}+\frac{21085148778264281865}{2147483648}\cdot t^{95}-\frac{43849645689310674675}{4294967296}\cdot t^{93}+\frac{2679839775126729517995}{274877906944}\cdot t^{91}-\frac{4707826631979389693775}{549755813888}\cdot t^{89}+\frac{7618119459021194231745}{1099511627776}\cdot t^{87}-\frac{11367923771917944802935}{2199023255552}\cdot t^{85}+\frac{250515357195969524360975}{70368744177664}\cdot t^{83}-\frac{318692994593601604261831}{140737488355328}\cdot t^{81}+\frac{187330424978822423404995}{140737488355328}\cdot t^{79}-\frac{203585551802381617816857}{281474976710656}\cdot t^{77}+\frac{3273029255899827547978701}{9007199254740992}\cdot t^{75}-\frac{3040728552099772830813825}{18014398509481984}\cdot t^{73}+\frac{2611449227097451960581285}{36028797018963968}\cdot t^{71}-\frac{2072644947089481993626475}{72057594037927936}\cdot t^{69}+\frac{97248500917438495140954207}{9223372036854775808}\cdot t^{67}-\frac{65814642035034133075191231}{18446744073709551616}\cdot t^{65}+\frac{5135596317259566206347455}{4611686018427387904}\cdot t^{63}-\frac{2954291489722513343445237}{9223372036854775808}\cdot t^{61}+\frac{100117656040596285527866365}{1180591620717411303424}\cdot t^{59}-\frac{48734369697143739555669801}{2361183241434822606848}\cdot t^{57}+\frac{21774931141276990014235443}{4722366482869645213696}\cdot t^{55}-\frac{8915294387867750253967365}{9444732965739290427392}\cdot t^{53}+\frac{53414242028181564565074039}{302231454903657293676544}\cdot t^{51}-\frac{18253325807003884969302975}{604462909807314587353088}\cdot t^{49}+\frac{2839406236645048773002685}{604462909807314587353088}\cdot t^{47}-\frac{802037664440370452996055}{1208925819614629174706176}\cdot t^{45}+\frac{3281063172710606398620225}{38685626227668133590597632}\cdot t^{43}-\frac{756781620678844847497845}{77371252455336267181195264}\cdot t^{41}+\frac{156865755550215564951525}{154742504910672534362390528}\cdot t^{39}-\frac{29095750904307818179995}{309485009821345068724781056}\cdot t^{37}+\frac{153791826208484181808545}{19807040628566084398385987584}\cdot t^{35}-\frac{22499664763719716787825}{39614081257132168796771975168}\cdot t^{33}+\frac{724379450929512833169}{19807040628566084398385987584}\cdot t^{31}-\frac{81538718151107109035}{39614081257132168796771975168}\cdot t^{29}+\frac{254651688994996048217}{2535301200456458802993406410752}\cdot t^{27}-\frac{21347681594756057541}{5070602400912917605986812821504}\cdot t^{25}+\frac{1520490142076642275}{10141204801825835211973625643008}\cdot t^{23}-\frac{90834476020163045}{20282409603651670423947251286016}\cdot t^{21}+\frac{71711428436970825}{649037107316853453566312041152512}\cdot t^{19}-\frac{2868457137478833}{1298074214633706907132624082305024}\cdot t^{17}+\frac{45446198823057}{1298074214633706907132624082305024}\cdot t^{15}-\frac{1107929156355}{2596148429267413814265248164610048}\cdot t^{13}+\frac{320068422947}{83076749736557242056487941267521536}\cdot t^{11}-\frac{4064595535}{166153499473114484112975882535043072}\cdot t^9+\frac{33715539}{332306998946228968225951765070086144}\cdot t^7-\frac{162877}{664613997892457936451903530140172288}\cdot t^5+\frac{47905}{170141183460469231731687303715884105728}\cdot t^3-\frac{33}{340282366920938463463374607431768211456}\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.