Rule: Q[18, 57, 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.

• $P_1$:
  $262144\cdot t^{18}-1114112\cdot t^{16}+1966080\cdot t^{14}-1863680\cdot t^{12}+1025024\cdot t^{10}-329472\cdot t^8+59136\cdot t^6-5280\cdot t^4+180\cdot t^2-1$
• $P_2$:
  $262144\cdot t^{75}-4849664\cdot t^{73}+43057152\cdot t^{71}-244285440\cdot t^{69}+994954240\cdot t^{67}-3098371584\cdot t^{65}+7672158208\cdot t^{63}-15511102464\cdot t^{61}+26089446240\cdot t^{59}-37014131440\cdot t^{57}+44753449832\cdot t^{55}-46474736364\cdot t^{53}+\frac{2668424446233}{64}\cdot t^{51}-\frac{4154140621425}{128}\cdot t^{49}+\frac{2814095259675}{128}\cdot t^{47}-\frac{3324630574545}{256}\cdot t^{45}+\frac{109712808959985}{16384}\cdot t^{43}-\frac{98774343460485}{32768}\cdot t^{41}+\frac{77581380878925}{65536}\cdot t^{39}-\frac{53081997443475}{131072}\cdot t^{37}+\frac{505037289962205}{4194304}\cdot t^{35}-\frac{260170725132045}{8388608}\cdot t^{33}+\frac{28907858348005}{4194304}\cdot t^{31}-\frac{11027197811175}{8388608}\cdot t^{29}+\frac{57397978350475}{268435456}\cdot t^{27}-\frac{15801325804719}{536870912}\cdot t^{25}+\frac{3646459801089}{1073741824}\cdot t^{23}-\frac{697319977079}{2147483648}\cdot t^{21}+\frac{3486599885395}{137438953472}\cdot t^{19}-\frac{437423756715}{274877906944}\cdot t^{17}+\frac{21554214099}{274877906944}\cdot t^{15}-\frac{1622360201}{549755813888}\cdot t^{13}+\frac{5752004349}{70368744177664}\cdot t^{11}-\frac{222945905}{140737488355328}\cdot t^9+\frac{5620485}{281474976710656}\cdot t^7-\frac{82251}{562949953421312}\cdot t^5+\frac{9139}{18014398509481984}\cdot t^3-\frac{19}{36028797018963968}\cdot t$
• $P_3$:
  $262144\cdot t^{151}-9830400\cdot t^{149}+180649984\cdot t^{147}-2168406016\cdot t^{145}+19120066560\cdot t^{143}-132058527744\cdot t^{141}+743959856640\cdot t^{139}-3514935460608\cdot t^{137}+14212299805132\cdot t^{135}-49941822741810\cdot t^{133}+\frac{308724873258879}{2}\cdot t^{131}-\frac{1694901544680435}{4}\cdot t^{129}+\frac{2082307612035963}{2}\cdot t^{127}-\frac{9220001773049109}{4}\cdot t^{125}+\frac{73969993520839125}{16}\cdot t^{123}-\frac{270071465395063725}{32}\cdot t^{121}+\frac{28834100570120038875}{2048}\cdot t^{119}-\frac{88210989151552415225}{4096}\cdot t^{117}+\frac{496351386718436724475}{16384}\cdot t^{115}-\frac{1287528033216997518375}{32768}\cdot t^{113}+\frac{6172331359240272951725}{131072}\cdot t^{111}-\frac{13697594673995589374875}{262144}\cdot t^{109}+\frac{56380449126669957384975}{1048576}\cdot t^{107}-\frac{107763237949897313222175}{2097152}\cdot t^{105}+\frac{49032273267203277516089625}{1073741824}\cdot t^{103}-\frac{81123316999250021036856315}{2147483648}\cdot t^{101}+\frac{250105464497077293184447125}{8589934592}\cdot t^{99}-\frac{359484920970465762737112001}{17179869184}\cdot t^{97}+\frac{482074248859011691043776923}{34359738368}\cdot t^{95}-\frac{603437488409163779229174085}{68719476736}\cdot t^{93}+\frac{1410658784379454998657052861}{274877906944}\cdot t^{91}-\frac{1540028718217506856705047045}{549755813888}\cdot t^{89}+\frac{100512541008995947514282737137}{70368744177664}\cdot t^{87}-\frac{95751824780915161612154754171}{140737488355328}\cdot t^{85}+\frac{170405789864340541852139816745}{562949953421312}\cdot t^{83}-\frac{141609500099719380689336214013}{1125899906842624}\cdot t^{81}+\frac{219738879465081797621383780365}{4503599627370496}\cdot t^{79}-\frac{159110572886466984364625952363}{9007199254740992}\cdot t^{77}+\frac{214938844074701013966249093543}{36028797018963968}\cdot t^{75}-\frac{135342703042272592184329755975}{72057594037927936}\cdot t^{73}+\frac{2540575882822088373288704276445}{4611686018427387904}\cdot t^{71}-\frac{1387240401848580445533383899575}{9223372036854775808}\cdot t^{69}+\frac{1408859732786480400528709362945}{36893488147419103232}\cdot t^{67}-\frac{664601849624687041939188479085}{73786976294838206464}\cdot t^{65}+\frac{145451583251194133757734852325}{73786976294838206464}\cdot t^{63}-\frac{58996249655157246776501799915}{147573952589676412928}\cdot t^{61}+\frac{44283485180040099098030473275}{590295810358705651712}\cdot t^{59}-\frac{15353402865865979646753827715}{1180591620717411303424}\cdot t^{57}+\frac{157077121627705791770635314315}{75557863725914323419136}\cdot t^{55}-\frac{46217460990121478260232502825}{151115727451828646838272}\cdot t^{53}+\frac{24975553429171528252000152507}{604462909807314587353088}\cdot t^{51}-\frac{6182067680488002042574295175}{1208925819614629174706176}\cdot t^{49}+\frac{2796196766251496308487450433}{4835703278458516698824704}\cdot t^{47}-\frac{576079417632526683719255559}{9671406556917033397649408}\cdot t^{45}+\frac{215539918161829711595639835}{38685626227668133590597632}\cdot t^{43}-\frac{36482201705741748748053003}{77371252455336267181195264}\cdot t^{41}+\frac{356135778556050404445279315}{9903520314283042199192993792}\cdot t^{39}-\frac{48734369697143739555669801}{19807040628566084398385987584}\cdot t^{37}+\frac{11906489441781999465911991}{79228162514264337593543950336}\cdot t^{35}-\frac{1291117408029941622419835}{158456325028528675187087900672}\cdot t^{33}+\frac{123498186855037894318419}{316912650057057350374175801344}\cdot t^{31}-\frac{10345281370490473943085}{633825300114114700748351602688}\cdot t^{29}+\frac{1505442378644850330069}{2535301200456458802993406410752}\cdot t^{27}-\frac{94241176191250662717}{5070602400912917605986812821504}\cdot t^{25}+\frac{642553474031254518525}{1298074214633706907132624082305024}\cdot t^{23}-\frac{28747308387251528415}{2596148429267413814265248164610048}\cdot t^{21}+\frac{2127179267555609925}{10384593717069655257060992658440192}\cdot t^{19}-\frac{63871405575418665}{20769187434139310514121985316880384}\cdot t^{17}+\frac{3041495503591365}{83076749736557242056487941267521536}\cdot t^{15}-\frac{55763406299475}{166153499473114484112975882535043072}\cdot t^{13}+\frac{1515521146815}{664613997892457936451903530140172288}\cdot t^{11}-\frac{14493768575}{1329227995784915872903807060280344576}\cdot t^9+\frac{2898753715}{85070591730234615865843651857942052864}\cdot t^7-\frac{10555545}{170141183460469231731687303715884105728}\cdot t^5+\frac{36575}{680564733841876926926749214863536422912}\cdot t^3-\frac{19}{1361129467683753853853498429727072845824}\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.