Rule: Q[1, 8, 36, 46, 90]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^9-\frac{9}{4}\cdot t^7+\frac{27}{16}\cdot t^5-\frac{15}{32}\cdot t^3+\frac{9}{256}\cdot t$
• $P_3$:
  $t^{45}-\frac{45}{4}\cdot t^{43}+\frac{945}{16}\cdot t^{41}-\frac{3075}{16}\cdot t^{39}+\frac{55575}{128}\cdot t^{37}-\frac{740259}{1024}\cdot t^{35}+\frac{3764565}{4096}\cdot t^{33}-\frac{934065}{1024}\cdot t^{31}+\frac{11738925}{16384}\cdot t^{29}-\frac{29419775}{65536}\cdot t^{27}+\frac{59007663}{262144}\cdot t^{25}-\frac{23666175}{262144}\cdot t^{23}+\frac{60480225}{2097152}\cdot t^{21}-\frac{488494125}{67108864}\cdot t^{19}+\frac{384942375}{268435456}\cdot t^{17}-\frac{29084535}{134217728}\cdot t^{15}+\frac{105306075}{4294967296}\cdot t^{13}-\frac{34512075}{17179869184}\cdot t^{11}+\frac{7811375}{68719476736}\cdot t^9-\frac{284625}{68719476736}\cdot t^7+\frac{47817}{549755813888}\cdot t^5-\frac{3795}{4398046511104}\cdot t^3+\frac{45}{17592186044416}\cdot t$
• $P_4$:
  $t^{91}-23\cdot t^{89}+\frac{4093}{16}\cdot t^{87}-\frac{14663}{8}\cdot t^{85}+\frac{2434145}{256}\cdot t^{83}-\frac{9742789}{256}\cdot t^{81}+\frac{125233803}{1024}\cdot t^{79}-\frac{82992897}{256}\cdot t^{77}+\frac{23685640407}{32768}\cdot t^{75}-\frac{45069663925}{32768}\cdot t^{73}+\frac{2368281785155}{1048576}\cdot t^{71}-\frac{1692675361195}{524288}\cdot t^{69}+\frac{67864001064965}{16777216}\cdot t^{67}-\frac{74930348189605}{16777216}\cdot t^{65}+\frac{73222247728025}{16777216}\cdot t^{63}-\frac{7942667146347}{2097152}\cdot t^{61}+\frac{3141949915241517}{1073741824}\cdot t^{59}-\frac{2165414329255587}{1073741824}\cdot t^{57}+\frac{21328109845237839}{17179869184}\cdot t^{55}-\frac{5868138362369745}{8589934592}\cdot t^{53}+\frac{92392123238841855}{274877906944}\cdot t^{51}-\frac{40638733321112355}{274877906944}\cdot t^{49}+\frac{63876229434821895}{1099511627776}\cdot t^{47}-\frac{5599712107651935}{274877906944}\cdot t^{45}+\frac{223933477310913825}{35184372088832}\cdot t^{43}-\frac{62203771906191531}{35184372088832}\cdot t^{41}+\frac{1961329250300137389}{4503599627370496}\cdot t^{39}-\frac{213549059302925857}{2251799813685248}\cdot t^{37}+\frac{1310495040775049143}{72057594037927936}\cdot t^{35}-\frac{220337146555501535}{72057594037927936}\cdot t^{33}+\frac{64616333879188399}{144115188075855872}\cdot t^{31}-\frac{513245006107757}{9007199254740992}\cdot t^{29}+\frac{114938592273312731}{18446744073709551616}\cdot t^{27}-\frac{10721296229571837}{18446744073709551616}\cdot t^{25}+\frac{13510911953468475}{295147905179352825856}\cdot t^{23}-\frac{443820648754665}{147573952589676412928}\cdot t^{21}+\frac{766908477350015}{4722366482869645213696}\cdot t^{19}-\frac{33429128211115}{4722366482869645213696}\cdot t^{17}+\frac{4600446448745}{18889465931478580854784}\cdot t^{15}-\frac{30349912775}{4722366482869645213696}\cdot t^{13}+\frac{75734705417}{604462909807314587353088}\cdot t^{11}-\frac{1036431451}{604462909807314587353088}\cdot t^9+\frac{296050227}{19342813113834066795298816}\cdot t^7-\frac{768867}{9671406556917033397649408}\cdot t^5+\frac{60765}{309485009821345068724781056}\cdot t^3-\frac{45}{309485009821345068724781056}\cdot t$
• $P_5$:
  $t^{181}-\frac{91}{2}\cdot t^{179}+1018\cdot t^{177}-\frac{59719}{4}\cdot t^{175}+\frac{41325725}{256}\cdot t^{173}-\frac{702635867}{512}\cdot t^{171}+\frac{9781786587}{1024}\cdot t^{169}-\frac{114660375609}{2048}\cdot t^{167}+\frac{18479184430161}{65536}\cdot t^{165}-\frac{162448349269635}{131072}\cdot t^{163}+\frac{630786417260571}{131072}\cdot t^{161}-\frac{2185053793604073}{131072}\cdot t^{159}+\frac{217815672201296571}{4194304}\cdot t^{157}-\frac{1228561427100871989}{8388608}\cdot t^{155}+\frac{6308941393332175455}{16777216}\cdot t^{153}-\frac{29638732625843663385}{33554432}\cdot t^{151}+\frac{4093146619517811985335}{2147483648}\cdot t^{149}-\frac{16285911738782348271645}{4294967296}\cdot t^{147}+\frac{14982285609945954452495}{2147483648}\cdot t^{145}-\frac{102259201856461393798075}{8589934592}\cdot t^{143}+\frac{20763477347206166410352515}{1099511627776}\cdot t^{141}-\frac{61372544325512343598439765}{2199023255552}\cdot t^{139}+\frac{169329082827888857738496905}{4398046511104}\cdot t^{137}-\frac{436824361111680738228008795}{8796093022208}\cdot t^{135}+\frac{16883903663225245736902163925}{281474976710656}\cdot t^{133}-\frac{38244592232790248936150130303}{562949953421312}\cdot t^{131}+\frac{40663421725453816726307828349}{562949953421312}\cdot t^{129}-\frac{10157848221629026338135935401}{140737488355328}\cdot t^{127}+\frac{305518594764172454219953919689}{4503599627370496}\cdot t^{125}-\frac{540676754527302874819775056375}{9007199254740992}\cdot t^{123}+\frac{901432936701862362141255174305}{18014398509481984}\cdot t^{121}-\frac{1416757011396138680895782471855}{36028797018963968}\cdot t^{119}+\frac{134411340400464944649515940653165}{4611686018427387904}\cdot t^{117}-\frac{188014688394459652150818310767135}{9223372036854775808}\cdot t^{115}+\frac{7758111357079417076780660154675}{576460752303423488}\cdot t^{113}-\frac{154767475561811886808437342188535}{18446744073709551616}\cdot t^{111}+\frac{5832082168148535471313821433248495}{1180591620717411303424}\cdot t^{109}-\frac{6487530465262002626326361151890265}{2361183241434822606848}\cdot t^{107}+\frac{6817739369547368915454266110844385}{4722366482869645213696}\cdot t^{105}-\frac{6768970081688582535311145120132075}{9444732965739290427392}\cdot t^{103}+\frac{101586319503070495168179274486119375}{302231454903657293676544}\cdot t^{101}-\frac{90012167676458563621019746051868925}{604462909807314587353088}\cdot t^{99}+\frac{37665817204586035766750636228620425}{604462909807314587353088}\cdot t^{97}-\frac{14883827147367778137125922982488225}{604462909807314587353088}\cdot t^{95}+\frac{177679673369291930808832775119272375}{19342813113834066795298816}\cdot t^{93}-\frac{125113885585626979486719177332608025}{38685626227668133590597632}\cdot t^{91}+\frac{83113209453252889885685193272064275}{77371252455336267181195264}\cdot t^{89}-\frac{52063876470335690191643022133447925}{154742504910672534362390528}\cdot t^{87}+\frac{983631165680784424876314514007761025}{9903520314283042199192993792}\cdot t^{85}-\frac{547024000442665784202344276408472875}{19807040628566084398385987584}\cdot t^{83}+\frac{71592617491684863610906347608656295}{9903520314283042199192993792}\cdot t^{81}-\frac{70510958327058786476434694421925065}{39614081257132168796771975168}\cdot t^{79}+\frac{8355034025851437780301439024000953005}{20282409603651670423947251286016}\cdot t^{77}-\frac{3631752195451373316975686099664994395}{40564819207303340847894502572032}\cdot t^{75}+\frac{1481112823970948835756597315584085375}{81129638414606681695789005144064}\cdot t^{73}-\frac{566127238506201126366816397194454893}{162259276829213363391578010288128}\cdot t^{71}+\frac{3241335331291348366562492995200976743}{5192296858534827628530496329220096}\cdot t^{69}-\frac{1084539192257463895800653724332930901}{10384593717069655257060992658440192}\cdot t^{67}+\frac{169429652026133620598777228777727747}{10384593717069655257060992658440192}\cdot t^{65}-\frac{12340382587538222164386045015639555}{5192296858534827628530496329220096}\cdot t^{63}+\frac{53553960740406308943346504591252671}{166153499473114484112975882535043072}\cdot t^{61}-\frac{13500166651486571519308632054108321}{332306998946228968225951765070086144}\cdot t^{59}+\frac{3157102492844051765082455912379087}{664613997892457936451903530140172288}\cdot t^{57}-\frac{683547019695990351064192261494033}{1329227995784915872903807060280344576}\cdot t^{55}+\frac{17500082241875399305761004645278555}{340282366920938463463374607431768211456}\cdot t^{53}-\frac{3225903294625309406375496528832665}{680564733841876926926749214863536422912}\cdot t^{51}+\frac{68327571792146282646963687434745}{170141183460469231731687303715884105728}\cdot t^{49}-\frac{42450546395124551113914823818885}{1361129467683753853853498429727072845824}\cdot t^{47}+\frac{192799210135591552011613944726555}{87112285931760246646623899502532662132736}\cdot t^{45}-\frac{24919630740183636109631251644525}{174224571863520493293247799005065324265472}\cdot t^{43}+\frac{2922212898439477250201491798845}{348449143727040986586495598010130648530944}\cdot t^{41}-\frac{309609360980182068588459562095}{696898287454081973172991196020261297061888}\cdot t^{39}+\frac{472029611758887579164052518415}{22300745198530623141535718272648361505980416}\cdot t^{37}-\frac{40244826181989222808129982685}{44601490397061246283071436545296723011960832}\cdot t^{35}+\frac{1526274541044378830057405325}{44601490397061246283071436545296723011960832}\cdot t^{33}-\frac{51163381683159373227747147}{44601490397061246283071436545296723011960832}\cdot t^{31}+\frac{48156893244246645973617657}{1427247692705959881058285969449495136382746624}\cdot t^{29}-\frac{2465072853899935152848919}{2854495385411919762116571938898990272765493248}\cdot t^{27}+\frac{108746506364062649520501}{5708990770823839524233143877797980545530986496}\cdot t^{25}-\frac{4088474693024731211475}{11417981541647679048466287755595961091061972992}\cdot t^{23}+\frac{4137281159164645219497}{730750818665451459101842416358141509827966271488}\cdot t^{21}-\frac{108339624028873315267}{1461501637330902918203684832716283019655932542976}\cdot t^{19}+\frac{576310750341874861}{730750818665451459101842416358141509827966271488}\cdot t^{17}-\frac{19469240161522493}{2923003274661805836407369665432566039311865085952}\cdot t^{15}+\frac{16223365729706995}{374144419156711147060143317175368453031918731001856}\cdot t^{13}-\frac{156699002270629}{748288838313422294120286634350736906063837462003712}\cdot t^{11}+\frac{1066045681129}{1496577676626844588240573268701473812127674924007424}\cdot t^9-\frac{4742958363}{2993155353253689176481146537402947624255349848014848}\cdot t^7+\frac{196829997}{95780971304118053647396689196894323976171195136475136}\cdot t^5-\frac{243015}{191561942608236107294793378393788647952342390272950272}\cdot t^3+\frac{45}{191561942608236107294793378393788647952342390272950272}\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.