Rule: Q[1, 90, 92]

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^{91}-45\cdot t^{89}+\frac{979}{2}\cdot t^{87}-\frac{13717}{4}\cdot t^{85}+\frac{2225895}{128}\cdot t^{83}-\frac{17413151}{256}\cdot t^{81}+\frac{54669195}{256}\cdot t^{79}-\frac{283085361}{512}\cdot t^{77}+\frac{19721613483}{16384}\cdot t^{75}-\frac{73263021975}{32768}\cdot t^{73}+\frac{234799050915}{65536}\cdot t^{71}-\frac{654854816525}{131072}\cdot t^{69}+\frac{51209646652255}{8388608}\cdot t^{67}-\frac{110247837145215}{16777216}\cdot t^{65}+\frac{26249485034575}{4194304}\cdot t^{63}-\frac{44385492876645}{8388608}\cdot t^{61}+\frac{2137511893796325}{536870912}\cdot t^{59}-\frac{2868457137478833}{1073741824}\cdot t^{57}+\frac{3436980173735899}{2147483648}\cdot t^{55}-\frac{3679823762074845}{4294967296}\cdot t^{53}+\frac{56342190490434849}{137438953472}\cdot t^{51}-\frac{48179941566267225}{274877906944}\cdot t^{49}+\frac{18395977688938395}{274877906944}\cdot t^{47}-\frac{12530593498262385}{549755813888}\cdot t^{45}+\frac{121620466306664325}{17592186044416}\cdot t^{43}-\frac{65566137955174857}{35184372088832}\cdot t^{41}+\frac{31331138183708265}{70368744177664}\cdot t^{39}-\frac{13228702788676823}{140737488355328}\cdot t^{37}+\frac{629308289804197437}{36028797018963968}\cdot t^{35}-\frac{204947144189106445}{72057594037927936}\cdot t^{33}+\frac{14544636039226909}{36028797018963968}\cdot t^{31}-\frac{3576549845711535}{72057594037927936}\cdot t^{29}+\frac{48402641245296107}{9223372036854775808}\cdot t^{27}-\frac{8725899885515631}{18446744073709551616}\cdot t^{25}+\frac{1327469556620025}{36893488147419103232}\cdot t^{23}-\frac{168345763320735}{73786976294838206464}\cdot t^{21}+\frac{280576272201225}{2361183241434822606848}\cdot t^{19}-\frac{23576679383985}{4722366482869645213696}\cdot t^{17}+\frac{781293468865}{4722366482869645213696}\cdot t^{15}-\frac{39688347475}{9444732965739290427392}\cdot t^{13}+\frac{23813008485}{302231454903657293676544}\cdot t^{11}-\frac{626358425}{604462909807314587353088}\cdot t^9+\frac{10737573}{1208925819614629174706176}\cdot t^7-\frac{107019}{2417851639229258349412352}\cdot t^5+\frac{16215}{154742504910672534362390528}\cdot t^3-\frac{23}{309485009821345068724781056}\cdot t$
• $P_3$:
  $2\cdot t^{183}-91\cdot t^{181}+\frac{8145}{4}\cdot t^{179}-\frac{238965}{8}\cdot t^{177}+\frac{10339219}{32}\cdot t^{175}-\frac{175882245}{64}\cdot t^{173}+\frac{4900329665}{256}\cdot t^{171}-\frac{57486918225}{512}\cdot t^{169}+\frac{18547370252775}{32768}\cdot t^{167}-\frac{163228634332517}{65536}\cdot t^{165}+\frac{2538486692550523}{262144}\cdot t^{163}-\frac{17612001997763823}{524288}\cdot t^{161}+\frac{109904353551937035}{1048576}\cdot t^{159}-\frac{621011509206424245}{2097152}\cdot t^{157}+\frac{6390678102304093533}{8388608}\cdot t^{155}-\frac{30087867120709805253}{16777216}\cdot t^{153}+\frac{4165020462852543041451}{1073741824}\cdot t^{151}-\frac{16614602586053205334425}{2147483648}\cdot t^{149}+\frac{122618880932946882207075}{8589934592}\cdot t^{147}-\frac{419720322581005739382495}{17179869184}\cdot t^{145}+\frac{2671878151064451170215395}{68719476736}\cdot t^{143}-\frac{7925088772350970707331845}{137438953472}\cdot t^{141}+\frac{43894851954603861325120825}{549755813888}\cdot t^{139}-\frac{113690392950744162562580025}{1099511627776}\cdot t^{137}+\frac{17652328345485543640549925215}{140737488355328}\cdot t^{135}-\frac{40167373555953897416043792093}{281474976710656}\cdot t^{133}+\frac{171659788254217775812089779451}{1125899906842624}\cdot t^{131}-\frac{344817904454980976890763027135}{2251799813685248}\cdot t^{129}+\frac{162935932874331670398931979855}{1125899906842624}\cdot t^{127}-\frac{290022335690217507199522752129}{2251799813685248}\cdot t^{125}+\frac{973018658700946182162901008225}{9007199254740992}\cdot t^{123}-\frac{1539228124864684630986347515225}{18014398509481984}\cdot t^{121}+\frac{147036791927863295012643196849125}{2305843009213693952}\cdot t^{119}-\frac{207173452965187275593772403186375}{4611686018427387904}\cdot t^{117}+\frac{551325118361474843991897854126565}{18446744073709551616}\cdot t^{115}-\frac{692988715409293883483583975800505}{36893488147419103232}\cdot t^{113}+\frac{1646108329996250636142687462036635}{147573952589676412928}\cdot t^{111}-\frac{1847672615301913979343832865551325}{295147905179352825856}\cdot t^{109}+\frac{3920476212569237809090771538080425}{1180591620717411303424}\cdot t^{107}-\frac{3931568629793129551786695913784985}{2361183241434822606848}\cdot t^{105}+\frac{119257581770391596404196442718144545}{151115727451828646838272}\cdot t^{103}-\frac{106849748770231461011639760122533395}{302231454903657293676544}\cdot t^{101}+\frac{180949440405656900774239030388596125}{1208925819614629174706176}\cdot t^{99}-\frac{144777459245891740995519303383651625}{2417851639229258349412352}\cdot t^{97}+\frac{109429196468972718518691213726344475}{4835703278458516698824704}\cdot t^{95}-\frac{78113726975853427367858716113209925}{9671406556917033397649408}\cdot t^{93}+\frac{105283718967454619495809573891717725}{38685626227668133590597632}\cdot t^{91}-\frac{66957109671024486230057494189561125}{77371252455336267181195264}\cdot t^{89}+\frac{1285313928782999451357378172776085125}{4951760157141521099596496896}\cdot t^{87}-\frac{726887287615601050268775773901033175}{9903520314283042199192993792}\cdot t^{85}+\frac{774623169190356940137172988903489085}{39614081257132168796771975168}\cdot t^{83}-\frac{388624892341852376129559145103725985}{79228162514264337593543950336}\cdot t^{81}+\frac{366883639623427068374059332790230825}{316912650057057350374175801344}\cdot t^{79}-\frac{162806926930689730327016679292337775}{633825300114114700748351602688}\cdot t^{77}+\frac{135718822848774401976310770259082715}{2535301200456458802993406410752}\cdot t^{75}-\frac{53082414856285971174667003166871675}{5070602400912917605986812821504}\cdot t^{73}+\frac{4982163794368554723108031582947812925}{2596148429267413814265248164610048}\cdot t^{71}-\frac{1710274489433051317436587717036236375}{5192296858534827628530496329220096}\cdot t^{69}+\frac{1098058005530908152902636777276138625}{20769187434139310514121985316880384}\cdot t^{67}-\frac{329194067827639040822743039262039661}{41538374868278621028243970633760768}\cdot t^{65}+\frac{46016375072680726136512467853833501}{41538374868278621028243970633760768}\cdot t^{63}-\frac{11977872919758157822818719141481651}{83076749736557242056487941267521536}\cdot t^{61}+\frac{5795744961173302172331638294265315}{332306998946228968225951765070086144}\cdot t^{59}-\frac{1300868375779551359944829217038955}{664613997892457936451903530140172288}\cdot t^{57}+\frac{34603098795736066174532457173236203}{170141183460469231731687303715884105728}\cdot t^{55}-\frac{6643258139840731515084770381674953}{340282366920938463463374607431768211456}\cdot t^{53}+\frac{2350901313996026714891323468399611}{1361129467683753853853498429727072845824}\cdot t^{51}-\frac{382370095081634655120096622299975}{2722258935367507707706996859454145691648}\cdot t^{49}+\frac{114012989811359623331955787988025}{10889035741470030830827987437816582766592}\cdot t^{47}-\frac{15532204409083774772759194305615}{21778071482940061661655974875633165533184}\cdot t^{45}+\frac{3853855229321538101511679790115}{87112285931760246646623899502532662132736}\cdot t^{43}-\frac{433756858042795575927339754515}{174224571863520493293247799005065324265472}\cdot t^{41}+\frac{1411431046012271318493724598025}{11150372599265311570767859136324180752990208}\cdot t^{39}-\frac{129071998654213630384283589675}{22300745198530623141535718272648361505980416}\cdot t^{37}+\frac{21120872507053139517428223765}{89202980794122492566142873090593446023921664}\cdot t^{35}-\frac{1537237815498057249280708641}{178405961588244985132285746181186892047843328}\cdot t^{33}+\frac{98886643102214209018057281}{356811923176489970264571492362373784095686656}\cdot t^{31}-\frac{5581052195961840902220735}{713623846352979940529142984724747568191373312}\cdot t^{29}+\frac{548114947160258201814615}{2854495385411919762116571938898990272765493248}\cdot t^{27}-\frac{23193290711663728612047}{5708990770823839524233143877797980545530986496}\cdot t^{25}+\frac{26761489282688917629285}{365375409332725729550921208179070754913983135744}\cdot t^{23}-\frac{811537431202240939735}{730750818665451459101842416358141509827966271488}\cdot t^{21}+\frac{40751520935550118925}{2923003274661805836407369665432566039311865085952}\cdot t^{19}-\frac{831266859117150225}{5846006549323611672814739330865132078623730171904}\cdot t^{17}+\frac{26917212580936293}{23384026197294446691258957323460528314494920687616}\cdot t^{15}-\frac{335865397623091}{46768052394588893382517914646921056628989841375232}\cdot t^{13}+\frac{6216777649407}{187072209578355573530071658587684226515959365500928}\cdot t^{11}-\frac{40516977215}{374144419156711147060143317175368453031918731001856}\cdot t^9+\frac{11050084695}{47890485652059026823698344598447161988085597568237568}\cdot t^7-\frac{27445509}{95780971304118053647396689196894323976171195136475136}\cdot t^5+\frac{64883}{383123885216472214589586756787577295904684780545900544}\cdot t^3-\frac{23}{766247770432944429179173513575154591809369561091801088}\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.