Rule: Q[2, 8, 20, 60, 91]

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.

• $P_1$:
  $2\cdot t^2-1$
• $P_2$:
  $2\cdot t^{10}-5\cdot t^8+\frac{35}{8}\cdot t^6-\frac{25}{16}\cdot t^4+\frac{25}{128}\cdot t^2-\frac{1}{256}$
• $P_3$:
  $2\cdot t^{30}-15\cdot t^{28}+\frac{405}{8}\cdot t^{26}-\frac{1625}{16}\cdot t^{24}+\frac{8625}{64}\cdot t^{22}-\frac{15939}{128}\cdot t^{20}+\frac{168245}{2048}\cdot t^{18}-\frac{159885}{4096}\cdot t^{16}+\frac{218025}{16384}\cdot t^{14}-\frac{104975}{32768}\cdot t^{12}+\frac{138567}{262144}\cdot t^{10}-\frac{29835}{524288}\cdot t^8+\frac{7735}{2097152}\cdot t^6-\frac{525}{4194304}\cdot t^4+\frac{225}{134217728}\cdot t^2-\frac{1}{268435456}$
• $P_4$:
  $2\cdot t^{90}-45\cdot t^{88}+\frac{3915}{8}\cdot t^{86}-\frac{54825}{16}\cdot t^{84}+\frac{2222325}{128}\cdot t^{82}-\frac{17365509}{256}\cdot t^{80}+\frac{108878985}{512}\cdot t^{78}-\frac{562760055}{1024}\cdot t^{76}+\frac{19559343375}{16384}\cdot t^{74}-\frac{72468842875}{32768}\cdot t^{72}+\frac{1852303623885}{524288}\cdot t^{70}-\frac{5147656215975}{1048576}\cdot t^{68}+\frac{50112653247825}{8388608}\cdot t^{66}-\frac{107384256959625}{16777216}\cdot t^{64}+\frac{50866226980875}{8388608}\cdot t^{62}-\frac{85500475751853}{16777216}\cdot t^{60}+\frac{2045078947037565}{536870912}\cdot t^{58}-\frac{2724025382315145}{1073741824}\cdot t^{56}+\frac{12947528051744825}{8589934592}\cdot t^{54}-\frac{13734553478166675}{17179869184}\cdot t^{52}+\frac{52034336891568603}{137438953472}\cdot t^{50}-\frac{43990381430070075}{274877906944}\cdot t^{48}+\frac{33169218083635725}{549755813888}\cdot t^{46}-\frac{22277833041247875}{1099511627776}\cdot t^{44}+\frac{106438535641517625}{17592186044416}\cdot t^{42}-\frac{56396048730674877}{35184372088832}\cdot t^{40}+\frac{845940730960123155}{2251799813685248}\cdot t^{38}-\frac{349615716557887465}{4503599627370496}\cdot t^{36}+\frac{507506685325965675}{36028797018963968}\cdot t^{34}-\frac{160944743057019075}{72057594037927936}\cdot t^{32}+\frac{22174609043411517}{72057594037927936}\cdot t^{30}-\frac{5273895535201755}{144115188075855872}\cdot t^{28}+\frac{34371250212176955}{9223372036854775808}\cdot t^{26}-\frac{5938679595405375}{18446744073709551616}\cdot t^{24}+\frac{3443436067924125}{147573952589676412928}\cdot t^{22}-\frac{413212328150895}{295147905179352825856}\cdot t^{20}+\frac{161543914297675}{2361183241434822606848}\cdot t^{18}-\frac{12603885205275}{4722366482869645213696}\cdot t^{16}+\frac{765418129875}{9444732965739290427392}\cdot t^{14}-\frac{35019130125}{18889465931478580854784}\cdot t^{12}+\frac{9245050353}{302231454903657293676544}\cdot t^{10}-\frac{207081765}{604462909807314587353088}\cdot t^8+\frac{23009085}{9671406556917033397649408}\cdot t^6-\frac{170775}{19342813113834066795298816}\cdot t^4+\frac{2025}{154742504910672534362390528}\cdot t^2-\frac{1}{309485009821345068724781056}$
• $P_5$:
  $2\cdot t^{181}-91\cdot t^{179}+2036\cdot t^{177}-\frac{59719}{2}\cdot t^{175}+\frac{41325725}{128}\cdot t^{173}-\frac{702635867}{256}\cdot t^{171}+\frac{9781786587}{512}\cdot t^{169}-\frac{114660375609}{1024}\cdot t^{167}+\frac{18479184430161}{32768}\cdot t^{165}-\frac{162448349269635}{65536}\cdot t^{163}+\frac{630786417260571}{65536}\cdot t^{161}-\frac{2185053793604073}{65536}\cdot t^{159}+\frac{217815672201296571}{2097152}\cdot t^{157}-\frac{1228561427100871989}{4194304}\cdot t^{155}+\frac{6308941393332175455}{8388608}\cdot t^{153}-\frac{29638732625843663385}{16777216}\cdot t^{151}+\frac{4093146619517811985335}{1073741824}\cdot t^{149}-\frac{16285911738782348271645}{2147483648}\cdot t^{147}+\frac{14982285609945954452495}{1073741824}\cdot t^{145}-\frac{102259201856461393798075}{4294967296}\cdot t^{143}+\frac{20763477347206166410352515}{549755813888}\cdot t^{141}-\frac{61372544325512343598439765}{1099511627776}\cdot t^{139}+\frac{169329082827888857738496905}{2199023255552}\cdot t^{137}-\frac{436824361111680738228008795}{4398046511104}\cdot t^{135}+\frac{16883903663225245736902163925}{140737488355328}\cdot t^{133}-\frac{38244592232790248936150130303}{281474976710656}\cdot t^{131}+\frac{40663421725453816726307828349}{281474976710656}\cdot t^{129}-\frac{10157848221629026338135935401}{70368744177664}\cdot t^{127}+\frac{305518594764172454219953919689}{2251799813685248}\cdot t^{125}-\frac{540676754527302874819775056375}{4503599627370496}\cdot t^{123}+\frac{901432936701862362141255174305}{9007199254740992}\cdot t^{121}-\frac{1416757011396138680895782471855}{18014398509481984}\cdot t^{119}+\frac{134411340400464944649515940653165}{2305843009213693952}\cdot t^{117}-\frac{188014688394459652150818310767135}{4611686018427387904}\cdot t^{115}+\frac{7758111357079417076780660154675}{288230376151711744}\cdot t^{113}-\frac{154767475561811886808437342188535}{9223372036854775808}\cdot t^{111}+\frac{5832082168148535471313821433248495}{590295810358705651712}\cdot t^{109}-\frac{6487530465262002626326361151890265}{1180591620717411303424}\cdot t^{107}+\frac{6817739369547368915454266110844385}{2361183241434822606848}\cdot t^{105}-\frac{6768970081688582535311145120132075}{4722366482869645213696}\cdot t^{103}+\frac{101586319503070495168179274486119375}{151115727451828646838272}\cdot t^{101}-\frac{90012167676458563621019746051868925}{302231454903657293676544}\cdot t^{99}+\frac{37665817204586035766750636228620425}{302231454903657293676544}\cdot t^{97}-\frac{14883827147367778137125922982488225}{302231454903657293676544}\cdot t^{95}+\frac{177679673369291930808832775119272375}{9671406556917033397649408}\cdot t^{93}-\frac{125113885585626979486719177332608025}{19342813113834066795298816}\cdot t^{91}+\frac{83113209453252889885685193272064275}{38685626227668133590597632}\cdot t^{89}-\frac{52063876470335690191643022133447925}{77371252455336267181195264}\cdot t^{87}+\frac{983631165680784424876314514007761025}{4951760157141521099596496896}\cdot t^{85}-\frac{547024000442665784202344276408472875}{9903520314283042199192993792}\cdot t^{83}+\frac{71592617491684863610906347608656295}{4951760157141521099596496896}\cdot t^{81}-\frac{70510958327058786476434694421925065}{19807040628566084398385987584}\cdot t^{79}+\frac{8355034025851437780301439024000953005}{10141204801825835211973625643008}\cdot t^{77}-\frac{3631752195451373316975686099664994395}{20282409603651670423947251286016}\cdot t^{75}+\frac{1481112823970948835756597315584085375}{40564819207303340847894502572032}\cdot t^{73}-\frac{566127238506201126366816397194454893}{81129638414606681695789005144064}\cdot t^{71}+\frac{3241335331291348366562492995200976743}{2596148429267413814265248164610048}\cdot t^{69}-\frac{1084539192257463895800653724332930901}{5192296858534827628530496329220096}\cdot t^{67}+\frac{169429652026133620598777228777727747}{5192296858534827628530496329220096}\cdot t^{65}-\frac{12340382587538222164386045015639555}{2596148429267413814265248164610048}\cdot t^{63}+\frac{53553960740406308943346504591252671}{83076749736557242056487941267521536}\cdot t^{61}-\frac{13500166651486571519308632054108321}{166153499473114484112975882535043072}\cdot t^{59}+\frac{3157102492844051765082455912379087}{332306998946228968225951765070086144}\cdot t^{57}-\frac{683547019695990351064192261494033}{664613997892457936451903530140172288}\cdot t^{55}+\frac{17500082241875399305761004645278555}{170141183460469231731687303715884105728}\cdot t^{53}-\frac{3225903294625309406375496528832665}{340282366920938463463374607431768211456}\cdot t^{51}+\frac{68327571792146282646963687434745}{85070591730234615865843651857942052864}\cdot t^{49}-\frac{42450546395124551113914823818885}{680564733841876926926749214863536422912}\cdot t^{47}+\frac{192799210135591552011613944726555}{43556142965880123323311949751266331066368}\cdot t^{45}-\frac{24919630740183636109631251644525}{87112285931760246646623899502532662132736}\cdot t^{43}+\frac{2922212898439477250201491798845}{174224571863520493293247799005065324265472}\cdot t^{41}-\frac{309609360980182068588459562095}{348449143727040986586495598010130648530944}\cdot t^{39}+\frac{472029611758887579164052518415}{11150372599265311570767859136324180752990208}\cdot t^{37}-\frac{40244826181989222808129982685}{22300745198530623141535718272648361505980416}\cdot t^{35}+\frac{1526274541044378830057405325}{22300745198530623141535718272648361505980416}\cdot t^{33}-\frac{51163381683159373227747147}{22300745198530623141535718272648361505980416}\cdot t^{31}+\frac{48156893244246645973617657}{713623846352979940529142984724747568191373312}\cdot t^{29}-\frac{2465072853899935152848919}{1427247692705959881058285969449495136382746624}\cdot t^{27}+\frac{108746506364062649520501}{2854495385411919762116571938898990272765493248}\cdot t^{25}-\frac{4088474693024731211475}{5708990770823839524233143877797980545530986496}\cdot t^{23}+\frac{4137281159164645219497}{365375409332725729550921208179070754913983135744}\cdot t^{21}-\frac{108339624028873315267}{730750818665451459101842416358141509827966271488}\cdot t^{19}+\frac{576310750341874861}{365375409332725729550921208179070754913983135744}\cdot t^{17}-\frac{19469240161522493}{1461501637330902918203684832716283019655932542976}\cdot t^{15}+\frac{16223365729706995}{187072209578355573530071658587684226515959365500928}\cdot t^{13}-\frac{156699002270629}{374144419156711147060143317175368453031918731001856}\cdot t^{11}+\frac{1066045681129}{748288838313422294120286634350736906063837462003712}\cdot t^9-\frac{4742958363}{1496577676626844588240573268701473812127674924007424}\cdot t^7+\frac{196829997}{47890485652059026823698344598447161988085597568237568}\cdot t^5-\frac{243015}{95780971304118053647396689196894323976171195136475136}\cdot t^3+\frac{45}{95780971304118053647396689196894323976171195136475136}\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.