Rule: Q[8, 80, 89]

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.

• $P_1$:
  $128\cdot t^8-256\cdot t^6+160\cdot t^4-32\cdot t^2+1$
• $P_2$:
  $128\cdot t^{88}-2816\cdot t^{86}+29920\cdot t^{84}-204512\cdot t^{82}+1010691\cdot t^{80}-3847932\cdot t^{78}+\frac{23486463}{2}\cdot t^{76}-\frac{59026825}{2}\cdot t^{74}+\frac{31886290865}{512}\cdot t^{72}-\frac{28657299385}{256}\cdot t^{70}+\frac{354909630845}{2048}\cdot t^{68}-\frac{477263364265}{2048}\cdot t^{66}+\frac{17960173971025}{65536}\cdot t^{64}-\frac{1160503548897}{4096}\cdot t^{62}+\frac{8473020119553}{32768}\cdot t^{60}-\frac{6848057356899}{32768}\cdot t^{58}+\frac{1257759867883783}{8388608}\cdot t^{56}-\frac{401191010054065}{4194304}\cdot t^{54}+\frac{1822553445674181}{33554432}\cdot t^{52}-\frac{921703229963373}{33554432}\cdot t^{50}+\frac{13283370078883905}{1073741824}\cdot t^{48}-\frac{1331169282958515}{268435456}\cdot t^{46}+\frac{3795482666286675}{2147483648}\cdot t^{44}-\frac{1200845017494045}{2147483648}\cdot t^{42}+\frac{344642520020790915}{2199023255552}\cdot t^{40}-\frac{42670026288288399}{1099511627776}\cdot t^{38}+\frac{74434313847808299}{8796093022208}\cdot t^{36}-\frac{14236070954498855}{8796093022208}\cdot t^{34}+\frac{76061293385465311}{281474976710656}\cdot t^{32}-\frac{1378083047895631}{35184372088832}\cdot t^{30}+\frac{1378083047895631}{281474976710656}\cdot t^{28}-\frac{147401073034677}{281474976710656}\cdot t^{26}+\frac{6843621248038575}{144115188075855872}\cdot t^{24}-\frac{260170725132045}{72057594037927936}\cdot t^{22}+\frac{130935593693905}{576460752303423488}\cdot t^{20}-\frac{6705596442545}{576460752303423488}\cdot t^{18}+\frac{8768856886405}{18446744073709551616}\cdot t^{16}-\frac{69704744725}{4611686018427387904}\cdot t^{14}+\frac{13353961621}{36893488147419103232}\cdot t^{12}-\frac{230602163}{36893488147419103232}\cdot t^{10}+\frac{691806489}{9444732965739290427392}\cdot t^8-\frac{2513049}{4722366482869645213696}\cdot t^6+\frac{78045}{37778931862957161709568}\cdot t^4-\frac{121}{37778931862957161709568}\cdot t^2+\frac{1}{1208925819614629174706176}$
• $P_3$:
  $128\cdot t^{177}-5696\cdot t^{175}+124592\cdot t^{173}-1785704\cdot t^{171}+18861585\cdot t^{169}-\frac{313148381}{2}\cdot t^{167}+\frac{8510335197}{8}\cdot t^{165}-\frac{97326660959}{16}\cdot t^{163}+\frac{3824170739829}{128}\cdot t^{161}-\frac{32769231701085}{256}\cdot t^{159}+\frac{495889009554411}{1024}\cdot t^{157}-\frac{3345601480915941}{2048}\cdot t^{155}+\frac{81152821787667903}{16384}\cdot t^{153}-\frac{445297018294859787}{32768}\cdot t^{151}+\frac{4446794263784286775}{131072}\cdot t^{149}-\frac{20301119215922726805}{262144}\cdot t^{147}+\frac{5445932761972879502795}{33554432}\cdot t^{145}-\frac{21032883492456638582115}{67108864}\cdot t^{143}+\frac{150163952971303045519745}{268435456}\cdot t^{141}-\frac{496822980814169305871575}{536870912}\cdot t^{139}+\frac{6108619120671886773126095}{4294967296}\cdot t^{137}-\frac{17482100604600809317442995}{8589934592}\cdot t^{135}+\frac{93338509084071455234525355}{34359738368}\cdot t^{133}-\frac{232814082566548526010051945}{68719476736}\cdot t^{131}+\frac{543389378110796077984694025}{137438953472}\cdot t^{129}-\frac{1188326950918297969996955283}{274877906944}\cdot t^{127}+\frac{4875483353476255859580460317}{1099511627776}\cdot t^{125}-\frac{9391639593875694552061633955}{2199023255552}\cdot t^{123}+\frac{68012490385920451725072978805}{17592186044416}\cdot t^{121}-\frac{115819592394014202432054286025}{35184372088832}\cdot t^{119}+\frac{371286326145287474970495843605}{140737488355328}\cdot t^{117}-\frac{560486526953626718139061908255}{281474976710656}\cdot t^{115}+\frac{51024344983122318401566871956915}{36028797018963968}\cdot t^{113}-\frac{68417309370402751372170334905435}{72057594037927936}\cdot t^{111}+\frac{173016073183708901663386261355425}{288230376151711744}\cdot t^{109}-\frac{206343887102222678892759875748615}{576460752303423488}\cdot t^{107}+\frac{928651498166099951612533008358635}{4611686018427387904}\cdot t^{105}-\frac{985827512546780209917405213170895}{9223372036854775808}\cdot t^{103}+\frac{1974911770333073949231366364673535}{36893488147419103232}\cdot t^{101}-\frac{1866491217441766154017427789947125}{73786976294838206464}\cdot t^{99}+\frac{6657180981892573244405214486081825}{590295810358705651712}\cdot t^{97}-\frac{5599609675555337390909824299260825}{1180591620717411303424}\cdot t^{95}+\frac{8884380876568970592590994304718175}{4722366482869645213696}\cdot t^{93}-\frac{6645381127442468969392710741767825}{9444732965739290427392}\cdot t^{91}+\frac{18740415826437066307843305498364875}{75557863725914323419136}\cdot t^{89}-\frac{12448302537001431009432384776489575}{151115727451828646838272}\cdot t^{87}+\frac{15573946933041332340166579000820275}{604462909807314587353088}\cdot t^{85}-\frac{9169620723823122869669873230992425}{1208925819614629174706176}\cdot t^{83}+\frac{1300092079470091208074558333278285325}{618970019642690137449562112}\cdot t^{81}-\frac{676848315336369800157873997743727125}{1237940039285380274899124224}\cdot t^{79}+\frac{661979477309762374617298456119219255}{4951760157141521099596496896}\cdot t^{77}-\frac{303816030624858108662474758469058321}{9903520314283042199192993792}\cdot t^{75}+\frac{522974677235201565907929512855052897}{79228162514264337593543950336}\cdot t^{73}-\frac{210812842359804438103760004679330653}{158456325028528675187087900672}\cdot t^{71}+\frac{159027372581312504755614581111263605}{633825300114114700748351602688}\cdot t^{69}-\frac{56056225488844534296515840495334423}{1267650600228229401496703205376}\cdot t^{67}+\frac{36884621793257125482743388415427601}{5070602400912917605986812821504}\cdot t^{65}-\frac{11309902702365746529402691663432797}{10141204801825835211973625643008}\cdot t^{63}+\frac{6454359051628831623532914912060291}{40564819207303340847894502572032}\cdot t^{61}-\frac{1710954066002447872550628615473565}{81129638414606681695789005144064}\cdot t^{59}+\frac{1682329739422939238941416577800243}{649037107316853453566312041152512}\cdot t^{57}-\frac{382726331725414163866007864178783}{1298074214633706907132624082305024}\cdot t^{55}+\frac{160812668480751542399000297779107}{5192296858534827628530496329220096}\cdot t^{53}-\frac{31125940905050035664453141432553}{10384593717069655257060992658440192}\cdot t^{51}+\frac{708625293569331937458469556207175}{2658455991569831745807614120560689152}\cdot t^{49}-\frac{115494057206147472208813241073135}{5316911983139663491615228241121378304}\cdot t^{47}+\frac{34391467430578502180348106852045}{21267647932558653966460912964485513216}\cdot t^{45}-\frac{4661831789158422131811340625115}{42535295865117307932921825928971026432}\cdot t^{43}+\frac{2292681194944671798881612004615}{340282366920938463463374607431768211456}\cdot t^{41}-\frac{254622423431232331236089365275}{680564733841876926926749214863536422912}\cdot t^{39}+\frac{50852573763557162331119743995}{2722258935367507707706996859454145691648}\cdot t^{37}-\frac{4542673367102596075137023145}{5444517870735015415413993718908291383296}\cdot t^{35}+\frac{1443758723086204494332198535}{43556142965880123323311949751266331066368}\cdot t^{33}-\frac{101377236006887695045390815}{87112285931760246646623899502532662132736}\cdot t^{31}+\frac{12490030210559268262659225}{348449143727040986586495598010130648530944}\cdot t^{29}-\frac{669389458677874948871319}{696898287454081973172991196020261297061888}\cdot t^{27}+\frac{123652917127145571570405}{5575186299632655785383929568162090376495104}\cdot t^{25}-\frac{4865995258543446734889}{11150372599265311570767859136324180752990208}\cdot t^{23}+\frac{322087223884589900397}{44601490397061246283071436545296723011960832}\cdot t^{21}-\frac{8826041066193003735}{89202980794122492566142873090593446023921664}\cdot t^{19}+\frac{12576296935888279659}{11417981541647679048466287755595961091061972992}\cdot t^{17}-\frac{222256791154438979}{22835963083295358096932575511191922182123945984}\cdot t^{15}+\frac{6054866885017601}{91343852333181432387730302044767688728495783936}\cdot t^{13}-\frac{61180092703639}{182687704666362864775460604089535377456991567872}\cdot t^{11}+\frac{1741556889215}{1461501637330902918203684832716283019655932542976}\cdot t^9-\frac{8104977507}{2923003274661805836407369665432566039311865085952}\cdot t^7+\frac{43977659}{11692013098647223345629478661730264157247460343808}\cdot t^5-\frac{56793}{23384026197294446691258957323460528314494920687616}\cdot t^3+\frac{11}{23384026197294446691258957323460528314494920687616}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Chebyshev T (first kind) type can be downloaded here packed into a single file.