Rule: Q[33, 66, 100]

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.

• $P_1$:
  $4294967296\cdot t^{33}-35433480192\cdot t^{31}+132875550720\cdot t^{29}-299708186624\cdot t^{27}+453437816832\cdot t^{25}-485826232320\cdot t^{23}+379364311040\cdot t^{21}-218864025600\cdot t^{19}+93564370944\cdot t^{17}-29455450112\cdot t^{15}+6723526656\cdot t^{13}-1083543552\cdot t^{11}+118243840\cdot t^9-8186112\cdot t^7+323136\cdot t^5-5984\cdot t^3+33\cdot t$
• $P_2$:
  $4294967296\cdot t^{99}-106300440576\cdot t^{97}+1275605286912\cdot t^{95}-9888155566080\cdot t^{93}+55659907252224\cdot t^{91}-242475872550912\cdot t^{89}+850838276800512\cdot t^{87}-2471262417321984\cdot t^{85}+6059345350164480\cdot t^{83}-12728365571981312\cdot t^{81}+23168485647876096\cdot t^{79}-36870921632802816\cdot t^{77}+51668734050565632\cdot t^{75}-64123764306940800\cdot t^{73}+70805568318756480\cdot t^{71}-69822157647662640\cdot t^{69}+61672734127039365\cdot t^{67}-\frac{195636176692803495}{4}\cdot t^{65}+34887109698305150\cdot t^{63}-\frac{358602764425210305}{16}\cdot t^{61}+\frac{830687416326752985}{64}\cdot t^{59}-\frac{1735416568174693965}{256}\cdot t^{57}+\frac{817510284181467405}{256}\cdot t^{55}-\frac{2778038379884391525}{2048}\cdot t^{53}+\frac{8506970861068203381}{16384}\cdot t^{51}-\frac{11725824700391307363}{65536}\cdot t^{49}+\frac{1816329010492647189}{32768}\cdot t^{47}-\frac{8080047984948772063}{524288}\cdot t^{45}+\frac{8047532701307127105}{2097152}\cdot t^{43}-\frac{7159529092887030321}{8388608}\cdot t^{41}+\frac{1418070979750571223}{8388608}\cdot t^{39}-\frac{1993910049326704509}{67108864}\cdot t^{37}+\frac{9910030543668546291}{2147483648}\cdot t^{35}-\frac{5414571325512199305}{8589934592}\cdot t^{33}+\frac{161702130083169753}{2147483648}\cdot t^{31}-\frac{2148328299676398147}{274877906944}\cdot t^{29}+\frac{769154576427352423}{1099511627776}\cdot t^{27}-\frac{235373370816042459}{4398046511104}\cdot t^{25}+\frac{15231236247802575}{4398046511104}\cdot t^{23}-\frac{6587184223408635}{35184372088832}\cdot t^{21}+\frac{2344590994772565}{281474976710656}\cdot t^{19}-\frac{337195172503035}{1125899906842624}\cdot t^{17}+\frac{4788903870135}{562949953421312}\cdot t^{15}-\frac{1670547861675}{9007199254740992}\cdot t^{13}+\frac{107688209265}{36028797018963968}\cdot t^{11}-\frac{4874774905}{144115188075855872}\cdot t^9+\frac{35990955}{144115188075855872}\cdot t^7-\frac{1237005}{1152921504606846976}\cdot t^5+\frac{40425}{18446744073709551616}\cdot t^3-\frac{99}{73786976294838206464}\cdot t$
• $P_3$:
  $4294967296\cdot t^{199}-214748364800\cdot t^{197}+5287910047744\cdot t^{195}-85483539398656\cdot t^{193}+1020463023128576\cdot t^{191}-9593451553226752\cdot t^{189}+73970749522575360\cdot t^{187}-481062074641809408\cdot t^{185}+2693177883448639488\cdot t^{183}-13182602545533943808\cdot t^{181}+57110024015256948736\cdot t^{179}-221140881801756200960\cdot t^{177}+771576039183912694784\cdot t^{175}-2442130677040136212480\cdot t^{173}+7052052547037678965280\cdot t^{171}-18669649764901757854560\cdot t^{169}+45504959645374736587275\cdot t^{167}-102488170908803499791790\cdot t^{165}+\frac{3423690138511024777285605}{16}\cdot t^{163}-\frac{6645204991092162626851005}{16}\cdot t^{161}+\frac{24040980794839363038729045}{32}\cdot t^{159}-\frac{2538702381746538238148775}{2}\cdot t^{157}+\frac{4110726564473543525200129245}{2048}\cdot t^{155}-\frac{6094289249294048348981778603}{2048}\cdot t^{153}+\frac{135748647876851633941707595023}{32768}\cdot t^{151}-\frac{88859844378188564352954735141}{16384}\cdot t^{149}+\frac{3505255273706154624447895358775}{524288}\cdot t^{147}-\frac{4073314114195821929504620556643}{524288}\cdot t^{145}+\frac{17866906659557441470589677674693}{2097152}\cdot t^{143}-\frac{4626440584004739511975250732907}{524288}\cdot t^{141}+\frac{579817744098412614095575760722467}{67108864}\cdot t^{139}-\frac{537062901448716006272186656670985}{67108864}\cdot t^{137}+\frac{30138696560497948501649790269927877}{4294967296}\cdot t^{135}-\frac{12515640532037304567999152826469941}{2147483648}\cdot t^{133}+\frac{315227279054970294251159158029893367}{68719476736}\cdot t^{131}-\frac{235234338364604650981431391188540039}{68719476736}\cdot t^{129}+\frac{83247425566389934057879123432128695}{34359738368}\cdot t^{127}-\frac{6987879611107051377195732694424351}{4294967296}\cdot t^{125}+\frac{4560278982258935900093990033707813825}{4398046511104}\cdot t^{123}-\frac{2758751257408759579647438242698004575}{4398046511104}\cdot t^{121}+\frac{25351285426627272835795483975587202025}{70368744177664}\cdot t^{119}-\frac{6912471724520593422194959077559427375}{35184372088832}\cdot t^{117}+\frac{114543704907372766647899733023295529725}{1125899906842624}\cdot t^{115}-\frac{56323765399835279915434096197119208825}{1125899906842624}\cdot t^{113}+\frac{105194408669652308184532991233552649925}{4503599627370496}\cdot t^{111}-\frac{11659026761602400396896625349200822025}{1125899906842624}\cdot t^{109}+\frac{628114784593335544504472192144267737125}{144115188075855872}\cdot t^{107}-\frac{250941081816003209892553959814234955175}{144115188075855872}\cdot t^{105}+\frac{3044596875035595187718673250384000008405}{4611686018427387904}\cdot t^{103}-\frac{547611751885579237610485035071575787265}{2305843009213693952}\cdot t^{101}+\frac{5979024057336329305189474058583378435315}{73786976294838206464}\cdot t^{99}-\frac{1934291698960459397840410483170737080875}{73786976294838206464}\cdot t^{97}+\frac{1186196499813796594468142080174620404445}{147573952589676412928}\cdot t^{95}-\frac{10767928234214172129130244225386249515}{4611686018427387904}\cdot t^{93}+\frac{6065890036214781187613649439625394230495}{9444732965739290427392}\cdot t^{91}-\frac{1579056286860392171064545148340413081865}{9444732965739290427392}\cdot t^{89}+\frac{6220593228414482356288021657569425363825}{151115727451828646838272}\cdot t^{87}-\frac{723841442052101794461012982821402013555}{75557863725914323419136}\cdot t^{85}+\frac{5091590937709864645717787507984193031585}{2417851639229258349412352}\cdot t^{83}-\frac{1056322514431951388702668402025112540485}{2417851639229258349412352}\cdot t^{81}+\frac{826645097477993541034880848747259061855}{9671406556917033397649408}\cdot t^{79}-\frac{38093273199634095136358571394226492325}{2417851639229258349412352}\cdot t^{77}+\frac{845960092468083393904126245105026107965}{309485009821345068724781056}\cdot t^{75}-\frac{138002335216770332928922059588891349575}{309485009821345068724781056}\cdot t^{73}+\frac{2706355740120326265427345873876292303475}{39614081257132168796771975168}\cdot t^{71}-\frac{194475174478690746404690827493700758475}{19807040628566084398385987584}\cdot t^{69}+\frac{837861385703346519330344961245060333625}{633825300114114700748351602688}\cdot t^{67}-\frac{105526784571810286487471890237253926425}{633825300114114700748351602688}\cdot t^{65}+\frac{12414283514781389753719751577563568225}{633825300114114700748351602688}\cdot t^{63}-\frac{170232704112485239351177387944952575}{79228162514264337593543950336}\cdot t^{61}+\frac{71202281201664010393252099709252254275}{324518553658426726783156020576256}\cdot t^{59}-\frac{6755068053837182567662015469903686125}{324518553658426726783156020576256}\cdot t^{57}+\frac{9506648500015588671127398847252125975}{5192296858534827628530496329220096}\cdot t^{55}-\frac{386757638699358542105061979294249593}{2596148429267413814265248164610048}\cdot t^{53}+\frac{929249997362332881209037257982267051}{83076749736557242056487941267521536}\cdot t^{51}-\frac{64213191389322131565142262717510751}{83076749736557242056487941267521536}\cdot t^{49}+\frac{16287934725287877643160033538048375}{332306998946228968225951765070086144}\cdot t^{47}-\frac{236212840143605931660974269006839}{83076749736557242056487941267521536}\cdot t^{45}+\frac{1598897744787160813033217689107003}{10633823966279326983230456482242756608}\cdot t^{43}-\frac{76786037994900132616359248167113}{10633823966279326983230456482242756608}\cdot t^{41}+\frac{106714139458503609032215616058357}{340282366920938463463374607431768211456}\cdot t^{39}-\frac{2085869663631001688532114503705}{170141183460469231731687303715884105728}\cdot t^{37}+\frac{2336616301477203136874757933323}{5444517870735015415413993718908291383296}\cdot t^{35}-\frac{72824297280201894887094583123}{5444517870735015415413993718908291383296}\cdot t^{33}+\frac{4015170109288647833264852111}{10889035741470030830827987437816582766592}\cdot t^{31}-\frac{6074176618645725835236607}{680564733841876926926749214863536422912}\cdot t^{29}+\frac{131082524256130409176630955}{696898287454081973172991196020261297061888}\cdot t^{27}-\frac{2382086588060374985907117}{696898287454081973172991196020261297061888}\cdot t^{25}+\frac{590569869366729970226145}{11150372599265311570767859136324180752990208}\cdot t^{23}-\frac{3850287569073385766235}{5575186299632655785383929568162090376495104}\cdot t^{21}+\frac{1330895739367651394665}{178405961588244985132285746181186892047843328}\cdot t^{19}-\frac{11685917970550989725}{178405961588244985132285746181186892047843328}\cdot t^{17}+\frac{325923666813535315}{713623846352979940529142984724747568191373312}\cdot t^{15}-\frac{438047104418245}{178405961588244985132285746181186892047843328}\cdot t^{13}+\frac{223672220014285}{22835963083295358096932575511191922182123945984}\cdot t^{11}-\frac{628581741095}{22835963083295358096932575511191922182123945984}\cdot t^9+\frac{73947021225}{1461501637330902918203684832716283019655932542976}\cdot t^7-\frac{39624585}{730750818665451459101842416358141509827966271488}\cdot t^5+\frac{646899}{23384026197294446691258957323460528314494920687616}\cdot t^3-\frac{99}{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.