Rule: Q[43, 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.

• $P_1$:
  $4398046511104\cdot t^{43}-47278999994368\cdot t^{41}+236394999971840\cdot t^{39}-729869562413056\cdot t^{37}+1557990796689408\cdot t^{35}-2439485589553152\cdot t^{33}+2901009890279424\cdot t^{31}-2676526982103040\cdot t^{29}+1940482062024704\cdot t^{27}-1112923535572992\cdot t^{25}+505874334351360\cdot t^{23}-181798588907520\cdot t^{21}+51314117836800\cdot t^{19}-11249633525760\cdot t^{17}+1884175073280\cdot t^{15}-235521884160\cdot t^{13}+21262392320\cdot t^{11}-1322886400\cdot t^9+52915456\cdot t^7-1218448\cdot t^5+13244\cdot t^3-43\cdot t$
• $P_2$:
  $4398046511104\cdot t^{87}-96757023244288\cdot t^{85}+1027768494063616\cdot t^{83}-7021206377070592\cdot t^{81}+34668632415928320\cdot t^{79}-131833918071504896\cdot t^{77}+401711242911154176\cdot t^{75}-1007640360685404160\cdot t^{73}+2121289813846917120\cdot t^{71}-3802303807933644800\cdot t^{69}+5866983249485496320\cdot t^{67}-7859650409428680704\cdot t^{65}+9202528147667419136\cdot t^{63}-9466658485564342272\cdot t^{61}+8590941486552842240\cdot t^{59}-6899134710656139264\cdot t^{57}+4914314202361999360\cdot t^{55}-3109888090887266304\cdot t^{53}+1750112349035052288\cdot t^{51}-876195558317164800\cdot t^{49}+390200429760173760\cdot t^{47}-154466412511031040\cdot t^{45}+\frac{217160000552617605}{4}\cdot t^{43}-\frac{67647602652164535}{4}\cdot t^{41}+\frac{298151153683675425}{64}\cdot t^{39}-\frac{36208289698311549}{32}\cdot t^{37}+\frac{247263912916191801}{1024}\cdot t^{35}-\frac{46165231018240817}{1024}\cdot t^{33}+\frac{15005344154945683}{2048}\cdot t^{31}-\frac{32968493968795}{32}\cdot t^{29}+\frac{8156405407879883}{65536}\cdot t^{27}-\frac{839333382817293}{65536}\cdot t^{25}+\frac{4661706374467415}{4194304}\cdot t^{23}-\frac{168538268481765}{2097152}\cdot t^{21}+\frac{320212591254325}{67108864}\cdot t^{19}-\frac{15333776480505}{67108864}\cdot t^{17}+\frac{2316478771061}{268435456}\cdot t^{15}-\frac{16765348991}{67108864}\cdot t^{13}+\frac{91743450617}{17179869184}\cdot t^{11}-\frac{1376030315}{17179869184}\cdot t^9+\frac{215320479}{274877906944}\cdot t^7-\frac{612535}{137438953472}\cdot t^5+\frac{53019}{4398046511104}\cdot t^3-\frac{43}{4398046511104}\cdot t$
• $P_3$:
  $4398046511104\cdot t^{173}-191315023233024\cdot t^{171}+4089083743698944\cdot t^{169}-57243324121088000\cdot t^{167}+590324683396612096\cdot t^{165}-4782368851994083328\cdot t^{163}+31695467152385507328\cdot t^{161}-176714357939783073792\cdot t^{159}+845868820810023567360\cdot t^{157}-3530270270993473732608\cdot t^{155}+13003377166228645740544\cdot t^{153}-42685798977263342977024\cdot t^{151}+125881290971346361384960\cdot t^{149}-335721758356708022681600\cdot t^{147}+814282963917475383869440\cdot t^{145}-1804786033309861618974720\cdot t^{143}+3670424626716889010027520\cdot t^{141}-6873748292351668447695360\cdot t^{139}+11890635585976713965190400\cdot t^{137}-19051549134272968772717440\cdot t^{135}+28340405398463940203222220\cdot t^{133}-39223483960762574783557170\cdot t^{131}+50600831174317087808147094\cdot t^{129}-60947233953806259790556280\cdot t^{127}+\frac{274552923584585501500022469}{4}\cdot t^{125}-\frac{578950179910115152871966715}{8}\cdot t^{123}+\frac{1144249405402374282530792205}{16}\cdot t^{121}-\frac{2121760242077189616325409635}{32}\cdot t^{119}+\frac{118221234685396436453361277875}{2048}\cdot t^{117}-\frac{193439902351895502467874558145}{4096}\cdot t^{115}+\frac{2325251553436587186859810615}{64}\cdot t^{113}-\frac{215430074099460794744170576345}{8192}\cdot t^{111}+\frac{18787314554062900848947640868315}{1048576}\cdot t^{109}-\frac{24106100904848315529620810880525}{2097152}\cdot t^{107}+\frac{29133949138925825059254114871365}{4194304}\cdot t^{105}-\frac{33172188966111727086420612333015}{8388608}\cdot t^{103}+\frac{569417545300906331850203653904205}{268435456}\cdot t^{101}-\frac{575648620437501130000689353405975}{536870912}\cdot t^{99}+\frac{274183356096857633884869759222875}{536870912}\cdot t^{97}-\frac{123049130700095635616338842744275}{536870912}\cdot t^{95}+\frac{1664779828937587687501184964615275}{17179869184}\cdot t^{93}-\frac{1325907303894023641089657180901925}{34359738368}\cdot t^{91}+\frac{994363454231232800054230333079175}{68719476736}\cdot t^{89}-\frac{701940656571528367792393875674625}{137438953472}\cdot t^{87}+\frac{119353772050545257876339427589313925}{70368744177664}\cdot t^{85}-\frac{74551923384585670005980226599545175}{140737488355328}\cdot t^{83}+\frac{10942162332187689028168316677301275}{70368744177664}\cdot t^{81}-\frac{12068158528717872702258861737405469}{281474976710656}\cdot t^{79}+\frac{199889727855744588583209961690962945}{18014398509481984}\cdot t^{77}-\frac{97036320708474257513450994990111783}{36028797018963968}\cdot t^{75}+\frac{44140595284782987321986797099553739}{72057594037927936}\cdot t^{73}-\frac{18796574505072855544688610202737393}{144115188075855872}\cdot t^{71}+\frac{119759839348233772832877656863254441}{4611686018427387904}\cdot t^{69}-\frac{44543781964332358530588747584048475}{9223372036854775808}\cdot t^{67}+\frac{7727531282564265848996911184710413}{9223372036854775808}\cdot t^{65}-\frac{624404848274706660123530035873917}{4611686018427387904}\cdot t^{63}+\frac{3003400000994061989478046060166019}{147573952589676412928}\cdot t^{61}-\frac{838421233665805254391564447344477}{295147905179352825856}\cdot t^{59}+\frac{216945241961295671721992419915395}{590295810358705651712}\cdot t^{57}-\frac{51930589895976933264269339675517}{1180591620717411303424}\cdot t^{55}+\frac{367198676538710118833372043881259}{75557863725914323419136}\cdot t^{53}-\frac{74725391910676055818814219084553}{151115727451828646838272}\cdot t^{51}+\frac{1746122517971246970666431693685}{37778931862957161709568}\cdot t^{49}-\frac{1196039892247793390353843757925}{302231454903657293676544}\cdot t^{47}+\frac{23941330603146554416523156692695}{77371252455336267181195264}\cdot t^{45}-\frac{3407666043091204275612737604945}{154742504910672534362390528}\cdot t^{43}+\frac{439810563993681035955597410865}{309485009821345068724781056}\cdot t^{41}-\frac{51260883345267183385006314315}{618970019642690137449562112}\cdot t^{39}+\frac{85931560989197611866618968325}{19807040628566084398385987584}\cdot t^{37}-\frac{8052139483548732527805354015}{39614081257132168796771975168}\cdot t^{35}+\frac{335483156279935712719015695}{39614081257132168796771975168}\cdot t^{33}-\frac{12349961260182680032043145}{39614081257132168796771975168}\cdot t^{31}+\frac{12760764771090717402101157}{1267650600228229401496703205376}\cdot t^{29}-\frac{716828639837233822387755}{2535301200456458802993406410752}\cdot t^{27}+\frac{34692479021141298889857}{5070602400912917605986812821504}\cdot t^{25}-\frac{1430521054354088327943}{10141204801825835211973625643008}\cdot t^{23}+\frac{3174538399386179131449}{1298074214633706907132624082305024}\cdot t^{21}-\frac{91128916723360487283}{2596148429267413814265248164610048}\cdot t^{19}+\frac{531300870240131925}{1298074214633706907132624082305024}\cdot t^{17}-\frac{19668445931249469}{5192296858534827628530496329220096}\cdot t^{15}+\frac{8978466407400063}{332306998946228968225951765070086144}\cdot t^{13}-\frac{95003806055801}{664613997892457936451903530140172288}\cdot t^{11}+\frac{707975095773}{1329227995784915872903807060280344576}\cdot t^9-\frac{3450031255}{2658455991569831745807614120560689152}\cdot t^7+\frac{156809003}{85070591730234615865843651857942052864}\cdot t^5-\frac{212033}{170141183460469231731687303715884105728}\cdot t^3+\frac{43}{170141183460469231731687303715884105728}\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.