Rule: Q[1, 2, 72, 76]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^3-1\cdot t$
• $P_3$:
  $2\cdot t^{75}-37\cdot t^{73}+\frac{657}{2}\cdot t^{71}-\frac{7455}{4}\cdot t^{69}+\frac{971635}{128}\cdot t^{67}-\frac{6051507}{256}\cdot t^{65}+\frac{3746171}{64}\cdot t^{63}-\frac{15147561}{128}\cdot t^{61}+\frac{815295195}{4096}\cdot t^{59}-\frac{2313383215}{8192}\cdot t^{57}+\frac{5594181229}{16384}\cdot t^{55}-\frac{11618684091}{32768}\cdot t^{53}+\frac{2668424446233}{8388608}\cdot t^{51}-\frac{4154140621425}{16777216}\cdot t^{49}+\frac{2814095259675}{16777216}\cdot t^{47}-\frac{3324630574545}{33554432}\cdot t^{45}+\frac{109712808959985}{2147483648}\cdot t^{43}-\frac{98774343460485}{4294967296}\cdot t^{41}+\frac{77581380878925}{8589934592}\cdot t^{39}-\frac{53081997443475}{17179869184}\cdot t^{37}+\frac{505037289962205}{549755813888}\cdot t^{35}-\frac{260170725132045}{1099511627776}\cdot t^{33}+\frac{28907858348005}{549755813888}\cdot t^{31}-\frac{11027197811175}{1099511627776}\cdot t^{29}+\frac{57397978350475}{35184372088832}\cdot t^{27}-\frac{15801325804719}{70368744177664}\cdot t^{25}+\frac{3646459801089}{140737488355328}\cdot t^{23}-\frac{697319977079}{281474976710656}\cdot t^{21}+\frac{3486599885395}{18014398509481984}\cdot t^{19}-\frac{437423756715}{36028797018963968}\cdot t^{17}+\frac{21554214099}{36028797018963968}\cdot t^{15}-\frac{1622360201}{72057594037927936}\cdot t^{13}+\frac{5752004349}{9223372036854775808}\cdot t^{11}-\frac{222945905}{18446744073709551616}\cdot t^9+\frac{5620485}{36893488147419103232}\cdot t^7-\frac{82251}{73786976294838206464}\cdot t^5+\frac{9139}{2361183241434822606848}\cdot t^3-\frac{19}{4722366482869645213696}\cdot t$
• $P_4$:
  $2\cdot t^{151}-75\cdot t^{149}+\frac{5513}{4}\cdot t^{147}-\frac{132349}{8}\cdot t^{145}+\frac{4667985}{32}\cdot t^{143}-\frac{64481703}{64}\cdot t^{141}+\frac{1453046595}{256}\cdot t^{139}-\frac{13730216643}{512}\cdot t^{137}+\frac{3553074951283}{32768}\cdot t^{135}-\frac{24970911370905}{65536}\cdot t^{133}+\frac{308724873258879}{262144}\cdot t^{131}-\frac{1694901544680435}{524288}\cdot t^{129}+\frac{2082307612035963}{262144}\cdot t^{127}-\frac{9220001773049109}{524288}\cdot t^{125}+\frac{73969993520839125}{2097152}\cdot t^{123}-\frac{270071465395063725}{4194304}\cdot t^{121}+\frac{28834100570120038875}{268435456}\cdot t^{119}-\frac{88210989151552415225}{536870912}\cdot t^{117}+\frac{496351386718436724475}{2147483648}\cdot t^{115}-\frac{1287528033216997518375}{4294967296}\cdot t^{113}+\frac{6172331359240272951725}{17179869184}\cdot t^{111}-\frac{13697594673995589374875}{34359738368}\cdot t^{109}+\frac{56380449126669957384975}{137438953472}\cdot t^{107}-\frac{107763237949897313222175}{274877906944}\cdot t^{105}+\frac{49032273267203277516089625}{140737488355328}\cdot t^{103}-\frac{81123316999250021036856315}{281474976710656}\cdot t^{101}+\frac{250105464497077293184447125}{1125899906842624}\cdot t^{99}-\frac{359484920970465762737112001}{2251799813685248}\cdot t^{97}+\frac{482074248859011691043776923}{4503599627370496}\cdot t^{95}-\frac{603437488409163779229174085}{9007199254740992}\cdot t^{93}+\frac{1410658784379454998657052861}{36028797018963968}\cdot t^{91}-\frac{1540028718217506856705047045}{72057594037927936}\cdot t^{89}+\frac{100512541008995947514282737137}{9223372036854775808}\cdot t^{87}-\frac{95751824780915161612154754171}{18446744073709551616}\cdot t^{85}+\frac{170405789864340541852139816745}{73786976294838206464}\cdot t^{83}-\frac{141609500099719380689336214013}{147573952589676412928}\cdot t^{81}+\frac{219738879465081797621383780365}{590295810358705651712}\cdot t^{79}-\frac{159110572886466984364625952363}{1180591620717411303424}\cdot t^{77}+\frac{214938844074701013966249093543}{4722366482869645213696}\cdot t^{75}-\frac{135342703042272592184329755975}{9444732965739290427392}\cdot t^{73}+\frac{2540575882822088373288704276445}{604462909807314587353088}\cdot t^{71}-\frac{1387240401848580445533383899575}{1208925819614629174706176}\cdot t^{69}+\frac{1408859732786480400528709362945}{4835703278458516698824704}\cdot t^{67}-\frac{664601849624687041939188479085}{9671406556917033397649408}\cdot t^{65}+\frac{145451583251194133757734852325}{9671406556917033397649408}\cdot t^{63}-\frac{58996249655157246776501799915}{19342813113834066795298816}\cdot t^{61}+\frac{44283485180040099098030473275}{77371252455336267181195264}\cdot t^{59}-\frac{15353402865865979646753827715}{154742504910672534362390528}\cdot t^{57}+\frac{157077121627705791770635314315}{9903520314283042199192993792}\cdot t^{55}-\frac{46217460990121478260232502825}{19807040628566084398385987584}\cdot t^{53}+\frac{24975553429171528252000152507}{79228162514264337593543950336}\cdot t^{51}-\frac{6182067680488002042574295175}{158456325028528675187087900672}\cdot t^{49}+\frac{2796196766251496308487450433}{633825300114114700748351602688}\cdot t^{47}-\frac{576079417632526683719255559}{1267650600228229401496703205376}\cdot t^{45}+\frac{215539918161829711595639835}{5070602400912917605986812821504}\cdot t^{43}-\frac{36482201705741748748053003}{10141204801825835211973625643008}\cdot t^{41}+\frac{356135778556050404445279315}{1298074214633706907132624082305024}\cdot t^{39}-\frac{48734369697143739555669801}{2596148429267413814265248164610048}\cdot t^{37}+\frac{11906489441781999465911991}{10384593717069655257060992658440192}\cdot t^{35}-\frac{1291117408029941622419835}{20769187434139310514121985316880384}\cdot t^{33}+\frac{123498186855037894318419}{41538374868278621028243970633760768}\cdot t^{31}-\frac{10345281370490473943085}{83076749736557242056487941267521536}\cdot t^{29}+\frac{1505442378644850330069}{332306998946228968225951765070086144}\cdot t^{27}-\frac{94241176191250662717}{664613997892457936451903530140172288}\cdot t^{25}+\frac{642553474031254518525}{170141183460469231731687303715884105728}\cdot t^{23}-\frac{28747308387251528415}{340282366920938463463374607431768211456}\cdot t^{21}+\frac{2127179267555609925}{1361129467683753853853498429727072845824}\cdot t^{19}-\frac{63871405575418665}{2722258935367507707706996859454145691648}\cdot t^{17}+\frac{3041495503591365}{10889035741470030830827987437816582766592}\cdot t^{15}-\frac{55763406299475}{21778071482940061661655974875633165533184}\cdot t^{13}+\frac{1515521146815}{87112285931760246646623899502532662132736}\cdot t^{11}-\frac{14493768575}{174224571863520493293247799005065324265472}\cdot t^9+\frac{2898753715}{11150372599265311570767859136324180752990208}\cdot t^7-\frac{10555545}{22300745198530623141535718272648361505980416}\cdot t^5+\frac{36575}{89202980794122492566142873090593446023921664}\cdot t^3-\frac{19}{178405961588244985132285746181186892047843328}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Chebyshev U (second kind) type can be downloaded here packed into a single file.