Rule: Q[1, 84, 86]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{85}-42\cdot t^{83}+\frac{3403}{8}\cdot t^{81}-\frac{5535}{2}\cdot t^{79}+\frac{415935}{32}\cdot t^{77}-\frac{1502501}{32}\cdot t^{75}+\frac{277962685}{2048}\cdot t^{73}-\frac{330237765}{1024}\cdot t^{71}+\frac{21042072975}{32768}\cdot t^{69}-\frac{35616668975}{32768}\cdot t^{67}+\frac{828931106355}{524288}\cdot t^{65}-\frac{65309723531}{32768}\cdot t^{63}+\frac{1149098108613}{524288}\cdot t^{61}-\frac{1107929156355}{524288}\cdot t^{59}+\frac{30089948992435}{16777216}\cdot t^{57}-\frac{11273135819701}{8388608}\cdot t^{55}+\frac{478303048350171}{536870912}\cdot t^{53}-\frac{280946973839103}{536870912}\cdot t^{51}+\frac{2341224781992525}{8589934592}\cdot t^{49}-\frac{270353529420975}{2147483648}\cdot t^{47}+\frac{1771225244267115}{34359738368}\cdot t^{45}-\frac{642312451217745}{34359738368}\cdot t^{43}+\frac{52728013040874885}{8796093022208}\cdot t^{41}-\frac{7459794805644825}{4398046511104}\cdot t^{39}+\frac{59437719903041025}{140737488355328}\cdot t^{37}-\frac{12978859493582073}{140737488355328}\cdot t^{35}+\frac{39602161018878633}{2251799813685248}\cdot t^{33}-\frac{820383749920273}{281474976710656}\cdot t^{31}+\frac{1879204156221315}{4503599627370496}\cdot t^{29}-\frac{230779457781565}{4503599627370496}\cdot t^{27}+\frac{771462758869803}{144115188075855872}\cdot t^{25}-\frac{33935311973745}{72057594037927936}\cdot t^{23}+\frac{317986441828055}{9223372036854775808}\cdot t^{21}-\frac{19090095135475}{9223372036854775808}\cdot t^{19}+\frac{14771069086725}{147573952589676412928}\cdot t^{17}-\frac{140676848445}{36893488147419103232}\cdot t^{15}+\frac{65649195941}{590295810358705651712}\cdot t^{13}-\frac{1412200023}{590295810358705651712}\cdot t^{11}+\frac{1362649145}{37778931862957161709568}\cdot t^9-\frac{6690585}{18889465931478580854784}\cdot t^7+\frac{1221759}{604462909807314587353088}\cdot t^5-\frac{3311}{604462909807314587353088}\cdot t^3+\frac{43}{9671406556917033397649408}\cdot t$
• $P_3$:
  $2\cdot t^{171}-85\cdot t^{169}+\frac{3549}{2}\cdot t^{167}-\frac{97027}{4}\cdot t^{165}+\frac{31256555}{128}\cdot t^{163}-\frac{494227899}{256}\cdot t^{161}+\frac{1597805055}{128}\cdot t^{159}-\frac{17376648741}{256}\cdot t^{157}+\frac{2595054152223}{8192}\cdot t^{155}-\frac{21112454878515}{16384}\cdot t^{153}+\frac{151540509461341}{32768}\cdot t^{151}-\frac{969054923574075}{65536}\cdot t^{149}+\frac{356159986244258365}{8388608}\cdot t^{147}-\frac{1849033774739785445}{16777216}\cdot t^{145}+\frac{4363452217062242325}{16777216}\cdot t^{143}-\frac{18811944951096792495}{33554432}\cdot t^{141}+\frac{2380434572658017204175}{2147483648}\cdot t^{139}-\frac{8664420488183318028555}{4294967296}\cdot t^{137}+\frac{29118954281354902869415}{8589934592}\cdot t^{135}-\frac{90602319048797762798025}{17179869184}\cdot t^{133}+\frac{4185827140054456641268755}{549755813888}\cdot t^{131}-\frac{11240087700272374109241075}{1099511627776}\cdot t^{129}+\frac{1757540985860771224354059}{137438953472}\cdot t^{127}-\frac{4103322272504240025111417}{274877906944}\cdot t^{125}+\frac{143246610864449820696457125}{8796093022208}\cdot t^{123}-\frac{292456958181215511479052465}{17592186044416}\cdot t^{121}+\frac{559335489039943259572687275}{35184372088832}\cdot t^{119}-\frac{1003089263997303097180035085}{70368744177664}\cdot t^{117}+\frac{54023521789569038233839032435}{4503599627370496}\cdot t^{115}-\frac{85392858772757426000196493275}{9007199254740992}\cdot t^{113}+\frac{63423240647184153958831386085}{9007199254740992}\cdot t^{111}-\frac{88583592805092486826507804175}{18014398509481984}\cdot t^{109}+\frac{7448614675011062535154641933915}{2305843009213693952}\cdot t^{107}-\frac{9208871554826190459311527012695}{4611686018427387904}\cdot t^{105}+\frac{10716206029273444140631060845975}{9223372036854775808}\cdot t^{103}-\frac{11739776907564838805158490641065}{18446744073709551616}\cdot t^{101}+\frac{193744684258831490085131953390125}{590295810358705651712}\cdot t^{99}-\frac{188159251919838149830425446625725}{1180591620717411303424}\cdot t^{97}+\frac{43012052088509742027222156298575}{590295810358705651712}\cdot t^{95}-\frac{37025026523076151561894530147125}{1180591620717411303424}\cdot t^{93}+\frac{479978980199150837520559999907275}{37778931862957161709568}\cdot t^{91}-\frac{365949343495721966048537181087375}{75557863725914323419136}\cdot t^{89}+\frac{262464767239788867957155970904425}{151115727451828646838272}\cdot t^{87}-\frac{177011122091950631878081933865775}{302231454903657293676544}\cdot t^{85}+\frac{28724077539466534354761477450037125}{154742504910672534362390528}\cdot t^{83}-\frac{17103768305652601296457271699470925}{309485009821345068724781056}\cdot t^{81}+\frac{4780556358722776759879361655131625}{309485009821345068724781056}\cdot t^{79}-\frac{2507045811272319182500138427142219}{618970019642690137449562112}\cdot t^{77}+\frac{39438795934316160903201102353860929}{39614081257132168796771975168}\cdot t^{75}-\frac{18158728839841935707048790282389925}{79228162514264337593543950336}\cdot t^{73}+\frac{7823137605099115907889216534773889}{158456325028528675187087900672}\cdot t^{71}-\frac{3150299294874623728910177133189615}{316912650057057350374175801344}\cdot t^{69}+\frac{18950261912245813507751988601186761}{10141204801825835211973625643008}\cdot t^{67}-\frac{6643258139840731515084770381674953}{20282409603651670423947251286016}\cdot t^{65}+\frac{271068285680883583478035200758865}{5070602400912917605986812821504}\cdot t^{63}-\frac{82268276912939493167459634356187}{10141204801825835211973625643008}\cdot t^{61}+\frac{370815139779998208119337760768035}{324518553658426726783156020576256}\cdot t^{59}-\frac{96790954105808838152888925808407}{649037107316853453566312041152512}\cdot t^{57}+\frac{23363333749677995416214568298581}{1298074214633706907132624082305024}\cdot t^{55}-\frac{5203922396620942431840203078355}{2596148429267413814265248164610048}\cdot t^{53}+\frac{34147643154969803195599046866539}{166153499473114484112975882535043072}\cdot t^{51}-\frac{6430105600736449427616125351475}{332306998946228968225951765070086144}\cdot t^{49}+\frac{554384471148538455049601423265}{332306998946228968225951765070086144}\cdot t^{47}-\frac{87270949950716480254640911395}{664613997892457936451903530140172288}\cdot t^{45}+\frac{1599967415763135471335083375575}{170141183460469231731687303715884105728}\cdot t^{43}-\frac{207731211564933332942570853795}{340282366920938463463374607431768211456}\cdot t^{41}+\frac{24348140863814370070455703275}{680564733841876926926749214863536422912}\cdot t^{39}-\frac{2564601617638443244094907765}{1361129467683753853853498429727072845824}\cdot t^{37}+\frac{3864309224767428055581919845}{43556142965880123323311949751266331066368}\cdot t^{35}-\frac{323521034013876416641514325}{87112285931760246646623899502532662132736}\cdot t^{33}+\frac{5981061133029648038750685}{43556142965880123323311949751266331066368}\cdot t^{31}-\frac{387838994123383954541775}{87112285931760246646623899502532662132736}\cdot t^{29}+\frac{349916959142430856764357}{2787593149816327892691964784081045188247552}\cdot t^{27}-\frac{16994721552372108859041}{5575186299632655785383929568162090376495104}\cdot t^{25}+\frac{703035916397081171775}{11150372599265311570767859136324180752990208}\cdot t^{23}-\frac{24449221559925984393}{22300745198530623141535718272648361505980416}\cdot t^{21}+\frac{45038039715653129145}{2854495385411919762116571938898990272765493248}\cdot t^{19}-\frac{1052837292054228993}{5708990770823839524233143877797980545530986496}\cdot t^{17}+\frac{9764448426034857}{5708990770823839524233143877797980545530986496}\cdot t^{15}-\frac{139549079179755}{11417981541647679048466287755595961091061972992}\cdot t^{13}+\frac{47325339895743}{730750818665451459101842416358141509827966271488}\cdot t^{11}-\frac{353126264315}{1461501637330902918203684832716283019655932542976}\cdot t^9+\frac{1722567143}{2923003274661805836407369665432566039311865085952}\cdot t^7-\frac{4896969}{5846006549323611672814739330865132078623730171904}\cdot t^5+\frac{105995}{187072209578355573530071658587684226515959365500928}\cdot t^3-\frac{43}{374144419156711147060143317175368453031918731001856}\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.