Rule: Q[2, 4, 36, 43, 84]

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.

• $P_1$:
  $2\cdot t^2-1$
• $P_2$:
  $2\cdot t^6-3\cdot t^4+\frac{9}{8}\cdot t^2-\frac{1}{16}$
• $P_3$:
  $2\cdot t^{42}-21\cdot t^{40}+\frac{819}{8}\cdot t^{38}-\frac{4921}{16}\cdot t^{36}+\frac{81585}{128}\cdot t^{34}-\frac{247401}{256}\cdot t^{32}+\frac{284053}{256}\cdot t^{30}-\frac{504339}{512}\cdot t^{28}+\frac{5607063}{8192}\cdot t^{26}-\frac{6135675}{16384}\cdot t^{24}+\frac{84672315}{524288}\cdot t^{22}-\frac{57358665}{1048576}\cdot t^{20}+\frac{121090515}{8388608}\cdot t^{18}-\frac{49142835}{16777216}\cdot t^{16}+\frac{15043725}{33554432}\cdot t^{14}-\frac{3380195}{67108864}\cdot t^{12}+\frac{8580495}{2147483648}\cdot t^{10}-\frac{908523}{4294967296}\cdot t^8+\frac{235543}{34359738368}\cdot t^6-\frac{8085}{68719476736}\cdot t^4+\frac{441}{549755813888}\cdot t^2-\frac{1}{1099511627776}$
• $P_4$:
  $2\cdot t^{85}-43\cdot t^{83}+446\cdot t^{81}-\frac{5945}{2}\cdot t^{79}+\frac{1831141}{128}\cdot t^{77}-\frac{13560547}{256}\cdot t^{75}+\frac{80384535}{512}\cdot t^{73}-\frac{391820565}{1024}\cdot t^{71}+\frac{25615811325}{32768}\cdot t^{69}-\frac{89004181207}{65536}\cdot t^{67}+\frac{132927690929}{65536}\cdot t^{65}-\frac{86056018529}{32768}\cdot t^{63}+\frac{3111484832911}{1048576}\cdot t^{61}-\frac{6167298918865}{2097152}\cdot t^{59}+\frac{10764573301519}{4194304}\cdot t^{57}-\frac{16594616082417}{8388608}\cdot t^{55}+\frac{724590381004479}{536870912}\cdot t^{53}-\frac{876386828841381}{1073741824}\cdot t^{51}+\frac{117537743465025}{268435456}\cdot t^{49}-\frac{447564281106705}{2147483648}\cdot t^{47}+\frac{48368073978063525}{549755813888}\cdot t^{45}-\frac{36183601418599635}{1099511627776}\cdot t^{43}+\frac{23947643403612915}{2199023255552}\cdot t^{41}-\frac{13992539490017025}{4398046511104}\cdot t^{39}+\frac{115172762172777855}{140737488355328}\cdot t^{37}-\frac{51988764864122541}{281474976710656}\cdot t^{35}+\frac{10253511006056829}{281474976710656}\cdot t^{33}-\frac{1758390578322763}{281474976710656}\cdot t^{31}+\frac{8341028974105135}{9007199254740992}\cdot t^{29}-\frac{2122571584427329}{18014398509481984}\cdot t^{27}+\frac{459760634073923}{36028797018963968}\cdot t^{25}-\frac{83925275384405}{72057594037927936}\cdot t^{23}+\frac{816426728002655}{9223372036854775808}\cdot t^{21}-\frac{101842634229525}{18446744073709551616}\cdot t^{19}+\frac{2560318641699}{9223372036854775808}\cdot t^{17}-\frac{405953191227}{36893488147419103232}\cdot t^{15}+\frac{789130130801}{2361183241434822606848}\cdot t^{13}-\frac{35385125399}{4722366482869645213696}\cdot t^{11}+\frac{1113061235}{9444732965739290427392}\cdot t^9-\frac{22825561}{18889465931478580854784}\cdot t^7+\frac{4356373}{604462909807314587353088}\cdot t^5-\frac{24703}{1208925819614629174706176}\cdot t^3+\frac{21}{1208925819614629174706176}\cdot t$
• $P_5$:
  $2\cdot t^{169}-85\cdot t^{167}+\frac{7097}{4}\cdot t^{165}-\frac{193971}{8}\cdot t^{163}+\frac{3903687}{16}\cdot t^{161}-\frac{61688277}{32}\cdot t^{159}+\frac{1594263055}{128}\cdot t^{157}-\frac{17322067009}{256}\cdot t^{155}+\frac{10336214969509}{32768}\cdot t^{153}-\frac{83983952800033}{65536}\cdot t^{151}+\frac{1203862308765545}{262144}\cdot t^{149}-\frac{7685495147818475}{524288}\cdot t^{147}+\frac{88106019581650665}{2097152}\cdot t^{145}-\frac{456457565669534205}{4194304}\cdot t^{143}+\frac{4298781916413501195}{16777216}\cdot t^{141}-\frac{18486268307834836285}{33554432}\cdot t^{139}+\frac{2332753902226009144925}{2147483648}\cdot t^{137}-\frac{8465291303699406798545}{4294967296}\cdot t^{135}+\frac{56713451632399765163373}{17179869184}\cdot t^{133}-\frac{175837359777625766488191}{34359738368}\cdot t^{131}+\frac{252896876173006581627111}{34359738368}\cdot t^{129}-\frac{338155057397222832806325}{34359738368}\cdot t^{127}+\frac{1684550276769409234506711}{137438953472}\cdot t^{125}-\frac{3914345899148481792160425}{274877906944}\cdot t^{123}+\frac{271919121092753518388254575}{17592186044416}\cdot t^{121}-\frac{552166019866599507586523955}{35184372088832}\cdot t^{119}+\frac{2099937191594866278987653475}{140737488355328}\cdot t^{117}-\frac{3742886294764448560532265385}{281474976710656}\cdot t^{115}+\frac{12516779638711841665436852885}{1125899906842624}\cdot t^{113}-\frac{19647876719263910894902019345}{2251799813685248}\cdot t^{111}+\frac{57942908449863927819106597215}{9007199254740992}\cdot t^{109}-\frac{80298536319048880839827410425}{18014398509481984}\cdot t^{107}+\frac{6696188995688295864630150814335}{2305843009213693952}\cdot t^{105}-\frac{8206197674647190557651133536715}{4611686018427387904}\cdot t^{103}+\frac{18921910772193488929707375072535}{18446744073709551616}\cdot t^{101}-\frac{20526079929594977975502589248925}{36893488147419103232}\cdot t^{99}+\frac{20952226917752659179146241620875}{73786976294838206464}\cdot t^{97}-\frac{20125165907313355056456776412925}{147573952589676412928}\cdot t^{95}+\frac{36377538203588629688640024831575}{590295810358705651712}\cdot t^{93}-\frac{30930653259771303749327761400025}{1180591620717411303424}\cdot t^{91}+\frac{6332603910779458742000798621180325}{604462909807314587353088}\cdot t^{89}-\frac{4762190342786024534249185016858625}{1208925819614629174706176}\cdot t^{87}+\frac{6732462389066815240276339379656025}{4835703278458516698824704}\cdot t^{85}-\frac{4471291652120253436272796994229851}{9671406556917033397649408}\cdot t^{83}+\frac{5577247213400820588651228320067109}{38685626227668133590597632}\cdot t^{81}-\frac{3264499385769899439534677106699513}{77371252455336267181195264}\cdot t^{79}+\frac{3584180987361304665922269932824575}{309485009821345068724781056}\cdot t^{77}-\frac{1843955058223452307075161331185801}{618970019642690137449562112}\cdot t^{75}+\frac{28425631318425917022948534437175135}{39614081257132168796771975168}\cdot t^{73}-\frac{12810371981773872346332933573795195}{79228162514264337593543950336}\cdot t^{71}+\frac{10790347173195260839991129715762783}{316912650057057350374175801344}\cdot t^{69}-\frac{4242058819552723291508836645045605}{633825300114114700748351602688}\cdot t^{67}+\frac{388698979414020332170360290531147}{316912650057057350374175801344}\cdot t^{65}-\frac{265278659742917992466602595617527}{1267650600228229401496703205376}\cdot t^{63}+\frac{168308183975521363477686888657213}{5070602400912917605986812821504}\cdot t^{61}-\frac{49554657650246967628722095441763}{10141204801825835211973625643008}\cdot t^{59}+\frac{432561343570207639532822190559695}{649037107316853453566312041152512}\cdot t^{57}-\frac{109106856422070570249836284940211}{1298074214633706907132624082305024}\cdot t^{55}+\frac{50787530545948124043290636202003}{5192296858534827628530496329220096}\cdot t^{53}-\frac{10881708434546989783742842583961}{10384593717069655257060992658440192}\cdot t^{51}+\frac{4281850878118059336202757256105}{41538374868278621028243970633760768}\cdot t^{49}-\frac{771426446693476117655738151525}{83076749736557242056487941267521536}\cdot t^{47}+\frac{253759279557514463158574692635}{332306998946228968225951765070086144}\cdot t^{45}-\frac{37974892287377540899612453245}{664613997892457936451903530140172288}\cdot t^{43}+\frac{659401950097852170068376304095}{170141183460469231731687303715884105728}\cdot t^{41}-\frac{80757481361616760868915074635}{340282366920938463463374607431768211456}\cdot t^{39}+\frac{17776904021397960166476959175}{1361129467683753853853498429727072845824}\cdot t^{37}-\frac{1749457689664487519539778445}{2722258935367507707706996859454145691648}\cdot t^{35}+\frac{153066713565237417485673021}{5444517870735015415413993718908291383296}\cdot t^{33}-\frac{11830406128296206918772207}{10889035741470030830827987437816582766592}\cdot t^{31}+\frac{1603717038961333513386333}{43556142965880123323311949751266331066368}\cdot t^{29}-\frac{94535069676316122865875}{87112285931760246646623899502532662132736}\cdot t^{27}+\frac{307217225016066477020337}{11150372599265311570767859136324180752990208}\cdot t^{25}-\frac{13288917386478971365245}{22300745198530623141535718272648361505980416}\cdot t^{23}+\frac{966606682164822932805}{89202980794122492566142873090593446023921664}\cdot t^{21}-\frac{29100075901383566079}{178405961588244985132285746181186892047843328}\cdot t^{19}+\frac{1423272479450827005}{713623846352979940529142984724747568191373312}\cdot t^{17}-\frac{27622570091602113}{1427247692705959881058285969449495136382746624}\cdot t^{15}+\frac{826257674199303}{5708990770823839524233143877797980545530986496}\cdot t^{13}-\frac{9165628449441}{11417981541647679048466287755595961091061972992}\cdot t^{11}+\frac{2291244796917}{730750818665451459101842416358141509827966271488}\cdot t^9-\frac{11704125065}{1461501637330902918203684832716283019655932542976}\cdot t^7+\frac{69701989}{5846006549323611672814739330865132078623730171904}\cdot t^5-\frac{98791}{11692013098647223345629478661730264157247460343808}\cdot t^3+\frac{21}{11692013098647223345629478661730264157247460343808}\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.