Rule: Q[1, 42, 44, 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.

• $P_1$:
  $t$
• $P_2$:
  $t^{43}-\frac{43}{4}\cdot t^{41}+\frac{215}{4}\cdot t^{39}-\frac{10621}{64}\cdot t^{37}+\frac{90687}{256}\cdot t^{35}-\frac{567987}{1024}\cdot t^{33}+\frac{168861}{256}\cdot t^{31}-\frac{1246355}{2048}\cdot t^{29}+\frac{7228859}{16384}\cdot t^{27}-\frac{16583853}{65536}\cdot t^{25}+\frac{7538115}{65536}\cdot t^{23}-\frac{173376645}{4194304}\cdot t^{21}+\frac{195747825}{16777216}\cdot t^{19}-\frac{171655785}{67108864}\cdot t^{17}+\frac{14375115}{33554432}\cdot t^{15}-\frac{14375115}{268435456}\cdot t^{13}+\frac{20764055}{4294967296}\cdot t^{11}-\frac{5167525}{17179869184}\cdot t^9+\frac{206701}{17179869184}\cdot t^7-\frac{76153}{274877906944}\cdot t^5+\frac{3311}{1099511627776}\cdot t^3-\frac{43}{4398046511104}\cdot t$
• $P_3$:
  $t^{87}-22\cdot t^{85}+\frac{3739}{16}\cdot t^{83}-\frac{25543}{16}\cdot t^{81}+\frac{504495}{64}\cdot t^{79}-\frac{479609}{16}\cdot t^{77}+\frac{374122749}{4096}\cdot t^{75}-\frac{938438215}{4096}\cdot t^{73}+\frac{31609681455}{65536}\cdot t^{71}-\frac{28329370975}{32768}\cdot t^{69}+\frac{1398797809955}{1048576}\cdot t^{67}-\frac{1873886682851}{1048576}\cdot t^{65}+\frac{2194053685109}{1048576}\cdot t^{63}-\frac{282128408121}{131072}\cdot t^{61}+\frac{65543681995795}{33554432}\cdot t^{59}-\frac{52636220631837}{33554432}\cdot t^{57}+\frac{1199783740811035}{1073741824}\cdot t^{55}-\frac{379625011094637}{536870912}\cdot t^{53}+\frac{6836376363418173}{17179869184}\cdot t^{51}-\frac{3422638899676425}{17179869184}\cdot t^{49}+\frac{6096881715002715}{68719476736}\cdot t^{47}-\frac{603384423871215}{17179869184}\cdot t^{45}+\frac{217160000552617605}{17592186044416}\cdot t^{43}-\frac{67647602652164535}{17592186044416}\cdot t^{41}+\frac{298151153683675425}{281474976710656}\cdot t^{39}-\frac{36208289698311549}{140737488355328}\cdot t^{37}+\frac{247263912916191801}{4503599627370496}\cdot t^{35}-\frac{46165231018240817}{4503599627370496}\cdot t^{33}+\frac{15005344154945683}{9007199254740992}\cdot t^{31}-\frac{32968493968795}{140737488355328}\cdot t^{29}+\frac{8156405407879883}{288230376151711744}\cdot t^{27}-\frac{839333382817293}{288230376151711744}\cdot t^{25}+\frac{4661706374467415}{18446744073709551616}\cdot t^{23}-\frac{168538268481765}{9223372036854775808}\cdot t^{21}+\frac{320212591254325}{295147905179352825856}\cdot t^{19}-\frac{15333776480505}{295147905179352825856}\cdot t^{17}+\frac{2316478771061}{1180591620717411303424}\cdot t^{15}-\frac{16765348991}{295147905179352825856}\cdot t^{13}+\frac{91743450617}{75557863725914323419136}\cdot t^{11}-\frac{1376030315}{75557863725914323419136}\cdot t^9+\frac{215320479}{1208925819614629174706176}\cdot t^7-\frac{612535}{604462909807314587353088}\cdot t^5+\frac{53019}{19342813113834066795298816}\cdot t^3-\frac{43}{19342813113834066795298816}\cdot t$
• $P_4$:
  $t^{173}-\frac{87}{2}\cdot t^{171}+\frac{3719}{4}\cdot t^{169}-\frac{104125}{8}\cdot t^{167}+\frac{34361419}{256}\cdot t^{165}-\frac{556741009}{512}\cdot t^{163}+\frac{3689838009}{512}\cdot t^{161}-\frac{20572258851}{512}\cdot t^{159}+\frac{3151106911935}{16384}\cdot t^{157}-\frac{26302563182961}{32768}\cdot t^{155}+\frac{193765419218371}{65536}\cdot t^{153}-\frac{1272135942496757}{131072}\cdot t^{151}+\frac{480199016461739965}{16777216}\cdot t^{149}-\frac{2561353747228302175}{33554432}\cdot t^{147}+\frac{3106242995901013885}{16777216}\cdot t^{145}-\frac{27538849385221277145}{67108864}\cdot t^{143}+\frac{3584399049528211923855}{4294967296}\cdot t^{141}-\frac{13425289633499352436905}{8589934592}\cdot t^{139}+\frac{46447795257721538926525}{17179869184}\cdot t^{137}-\frac{148840227611507568536855}{34359738368}\cdot t^{135}+\frac{7085101349615985050805555}{1099511627776}\cdot t^{133}-\frac{19611741980381287391778585}{2199023255552}\cdot t^{131}+\frac{25300415587158543904073547}{2199023255552}\cdot t^{129}-\frac{7618404244225782473819535}{549755813888}\cdot t^{127}+\frac{274552923584585501500022469}{17592186044416}\cdot t^{125}-\frac{578950179910115152871966715}{35184372088832}\cdot t^{123}+\frac{1144249405402374282530792205}{70368744177664}\cdot t^{121}-\frac{2121760242077189616325409635}{140737488355328}\cdot t^{119}+\frac{118221234685396436453361277875}{9007199254740992}\cdot t^{117}-\frac{193439902351895502467874558145}{18014398509481984}\cdot t^{115}+\frac{2325251553436587186859810615}{281474976710656}\cdot t^{113}-\frac{215430074099460794744170576345}{36028797018963968}\cdot t^{111}+\frac{18787314554062900848947640868315}{4611686018427387904}\cdot t^{109}-\frac{24106100904848315529620810880525}{9223372036854775808}\cdot t^{107}+\frac{29133949138925825059254114871365}{18446744073709551616}\cdot t^{105}-\frac{33172188966111727086420612333015}{36893488147419103232}\cdot t^{103}+\frac{569417545300906331850203653904205}{1180591620717411303424}\cdot t^{101}-\frac{575648620437501130000689353405975}{2361183241434822606848}\cdot t^{99}+\frac{274183356096857633884869759222875}{2361183241434822606848}\cdot t^{97}-\frac{123049130700095635616338842744275}{2361183241434822606848}\cdot t^{95}+\frac{1664779828937587687501184964615275}{75557863725914323419136}\cdot t^{93}-\frac{1325907303894023641089657180901925}{151115727451828646838272}\cdot t^{91}+\frac{994363454231232800054230333079175}{302231454903657293676544}\cdot t^{89}-\frac{701940656571528367792393875674625}{604462909807314587353088}\cdot t^{87}+\frac{119353772050545257876339427589313925}{309485009821345068724781056}\cdot t^{85}-\frac{74551923384585670005980226599545175}{618970019642690137449562112}\cdot t^{83}+\frac{10942162332187689028168316677301275}{309485009821345068724781056}\cdot t^{81}-\frac{12068158528717872702258861737405469}{1237940039285380274899124224}\cdot t^{79}+\frac{199889727855744588583209961690962945}{79228162514264337593543950336}\cdot t^{77}-\frac{97036320708474257513450994990111783}{158456325028528675187087900672}\cdot t^{75}+\frac{44140595284782987321986797099553739}{316912650057057350374175801344}\cdot t^{73}-\frac{18796574505072855544688610202737393}{633825300114114700748351602688}\cdot t^{71}+\frac{119759839348233772832877656863254441}{20282409603651670423947251286016}\cdot t^{69}-\frac{44543781964332358530588747584048475}{40564819207303340847894502572032}\cdot t^{67}+\frac{7727531282564265848996911184710413}{40564819207303340847894502572032}\cdot t^{65}-\frac{624404848274706660123530035873917}{20282409603651670423947251286016}\cdot t^{63}+\frac{3003400000994061989478046060166019}{649037107316853453566312041152512}\cdot t^{61}-\frac{838421233665805254391564447344477}{1298074214633706907132624082305024}\cdot t^{59}+\frac{216945241961295671721992419915395}{2596148429267413814265248164610048}\cdot t^{57}-\frac{51930589895976933264269339675517}{5192296858534827628530496329220096}\cdot t^{55}+\frac{367198676538710118833372043881259}{332306998946228968225951765070086144}\cdot t^{53}-\frac{74725391910676055818814219084553}{664613997892457936451903530140172288}\cdot t^{51}+\frac{1746122517971246970666431693685}{166153499473114484112975882535043072}\cdot t^{49}-\frac{1196039892247793390353843757925}{1329227995784915872903807060280344576}\cdot t^{47}+\frac{23941330603146554416523156692695}{340282366920938463463374607431768211456}\cdot t^{45}-\frac{3407666043091204275612737604945}{680564733841876926926749214863536422912}\cdot t^{43}+\frac{439810563993681035955597410865}{1361129467683753853853498429727072845824}\cdot t^{41}-\frac{51260883345267183385006314315}{2722258935367507707706996859454145691648}\cdot t^{39}+\frac{85931560989197611866618968325}{87112285931760246646623899502532662132736}\cdot t^{37}-\frac{8052139483548732527805354015}{174224571863520493293247799005065324265472}\cdot t^{35}+\frac{335483156279935712719015695}{174224571863520493293247799005065324265472}\cdot t^{33}-\frac{12349961260182680032043145}{174224571863520493293247799005065324265472}\cdot t^{31}+\frac{12760764771090717402101157}{5575186299632655785383929568162090376495104}\cdot t^{29}-\frac{716828639837233822387755}{11150372599265311570767859136324180752990208}\cdot t^{27}+\frac{34692479021141298889857}{22300745198530623141535718272648361505980416}\cdot t^{25}-\frac{1430521054354088327943}{44601490397061246283071436545296723011960832}\cdot t^{23}+\frac{3174538399386179131449}{5708990770823839524233143877797980545530986496}\cdot t^{21}-\frac{91128916723360487283}{11417981541647679048466287755595961091061972992}\cdot t^{19}+\frac{531300870240131925}{5708990770823839524233143877797980545530986496}\cdot t^{17}-\frac{19668445931249469}{22835963083295358096932575511191922182123945984}\cdot t^{15}+\frac{8978466407400063}{1461501637330902918203684832716283019655932542976}\cdot t^{13}-\frac{95003806055801}{2923003274661805836407369665432566039311865085952}\cdot t^{11}+\frac{707975095773}{5846006549323611672814739330865132078623730171904}\cdot t^9-\frac{3450031255}{11692013098647223345629478661730264157247460343808}\cdot t^7+\frac{156809003}{374144419156711147060143317175368453031918731001856}\cdot t^5-\frac{212033}{748288838313422294120286634350736906063837462003712}\cdot t^3+\frac{43}{748288838313422294120286634350736906063837462003712}\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.