Rule: Q[1, 2, 64, 68]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^3-1\cdot t$
• $P_3$:
  $2\cdot t^{67}-33\cdot t^{65}+260\cdot t^{63}-1302\cdot t^{61}+\frac{595665}{128}\cdot t^{59}-\frac{3235501}{256}\cdot t^{57}+\frac{13881343}{512}\cdot t^{55}-\frac{48275865}{1024}\cdot t^{53}+\frac{2217471399}{32768}\cdot t^{51}-\frac{5324436975}{65536}\cdot t^{49}+\frac{5397877485}{65536}\cdot t^{47}-\frac{9306388455}{131072}\cdot t^{45}+\frac{219364870725}{4194304}\cdot t^{43}-\frac{277044025545}{8388608}\cdot t^{41}+\frac{300497488025}{16777216}\cdot t^{39}-\frac{280086337895}{33554432}\cdot t^{37}+\frac{7174519270695}{2147483648}\cdot t^{35}-\frac{4923689695575}{4294967296}\cdot t^{33}+\frac{722141155351}{2147483648}\cdot t^{31}-\frac{360682746765}{4294967296}\cdot t^{29}+\frac{4881239839553}{274877906944}\cdot t^{27}-\frac{1735881645069}{549755813888}\cdot t^{25}+\frac{514589420475}{1099511627776}\cdot t^{23}-\frac{125788525005}{2199023255552}\cdot t^{21}+\frac{400236215925}{70368744177664}\cdot t^{19}-\frac{63665481789}{140737488355328}\cdot t^{17}+\frac{3964517181}{140737488355328}\cdot t^{15}-\frac{376038215}{281474976710656}\cdot t^{13}+\frac{419014011}{9007199254740992}\cdot t^{11}-\frac{20376455}{18014398509481984}\cdot t^9+\frac{643467}{36028797018963968}\cdot t^7-\frac{11781}{72057594037927936}\cdot t^5+\frac{6545}{9223372036854775808}\cdot t^3-\frac{17}{18446744073709551616}\cdot t$
• $P_4$:
  $2\cdot t^{135}-67\cdot t^{133}+\frac{4389}{4}\cdot t^{131}-\frac{93665}{8}\cdot t^{129}+\frac{366145}{4}\cdot t^{127}-\frac{4472559}{8}\cdot t^{125}+\frac{88877775}{32}\cdot t^{123}-\frac{738482775}{64}\cdot t^{121}+\frac{1340346236625}{32768}\cdot t^{119}-\frac{8233220408875}{65536}\cdot t^{117}+\frac{88683545547025}{262144}\cdot t^{115}-\frac{422778648044181}{524288}\cdot t^{113}+\frac{3595891511859647}{2097152}\cdot t^{111}-\frac{13729154271359065}{4194304}\cdot t^{109}+\frac{94625060938196085}{16777216}\cdot t^{107}-\frac{295657697289537189}{33554432}\cdot t^{105}+\frac{26904850453347884199}{2147483648}\cdot t^{103}-\frac{69862174706592405189}{4294967296}\cdot t^{101}+\frac{332207139612327350475}{17179869184}\cdot t^{99}-\frac{724937847170220412575}{34359738368}\cdot t^{97}+\frac{1454875265700235448685}{68719476736}\cdot t^{95}-\frac{2689862551284286243635}{137438953472}\cdot t^{93}+\frac{9176421048161225319195}{549755813888}\cdot t^{91}-\frac{14458424083193619731475}{1099511627776}\cdot t^{89}+\frac{674037960830788272243525}{70368744177664}\cdot t^{87}-\frac{908676040168641054581271}{140737488355328}\cdot t^{85}+\frac{2268512911469964031367229}{562949953421312}\cdot t^{83}-\frac{2623088493962720896616609}{1125899906842624}\cdot t^{81}+\frac{5620903915634401921321305}{4503599627370496}\cdot t^{79}-\frac{5581052195961840902220735}{9007199254740992}\cdot t^{77}+\frac{10270540078858079547105579}{36028797018963968}\cdot t^{75}-\frac{8755990389809883484859595}{72057594037927936}\cdot t^{73}+\frac{442514283546545649965596455}{9223372036854775808}\cdot t^{71}-\frac{323521034013876416641514325}{18446744073709551616}\cdot t^{69}+\frac{437704928371715151926754675}{73786976294838206464}\cdot t^{67}-\frac{273766788296990721615291255}{147573952589676412928}\cdot t^{65}+\frac{79088183285797319577750807}{147573952589676412928}\cdot t^{63}-\frac{42167409761715032796982617}{295147905179352825856}\cdot t^{61}+\frac{41442728176121648774692905}{1180591620717411303424}\cdot t^{59}-\frac{18743988345055284444488385}{2361183241434822606848}\cdot t^{57}+\frac{498590089978470566223391041}{302231454903657293676544}\cdot t^{55}-\frac{190091472045707006634591963}{604462909807314587353088}\cdot t^{53}+\frac{132698099533426674337622961}{2417851639229258349412352}\cdot t^{51}-\frac{42308096250342338029624725}{4835703278458516698824704}\cdot t^{49}+\frac{24582174501187050159505275}{19342813113834066795298816}\cdot t^{47}-\frac{6489213830472088210604445}{38685626227668133590597632}\cdot t^{45}+\frac{3103537049356216100723865}{154742504910672534362390528}\cdot t^{43}-\frac{669972258084786789135465}{309485009821345068724781056}\cdot t^{41}+\frac{4161948875981251265841525}{19807040628566084398385987584}\cdot t^{39}-\frac{723435167042483506448175}{39614081257132168796771975168}\cdot t^{37}+\frac{224096661046648379206737}{158456325028528675187087900672}\cdot t^{35}-\frac{30758365241696836361709}{316912650057057350374175801344}\cdot t^{33}+\frac{3718044150095221977789}{633825300114114700748351602688}\cdot t^{31}-\frac{393018988359690434115}{1267650600228229401496703205376}\cdot t^{29}+\frac{72071232734432843835}{5070602400912917605986812821504}\cdot t^{27}-\frac{5678339548773496787}{10141204801825835211973625643008}\cdot t^{25}+\frac{12167870461657493115}{649037107316853453566312041152512}\cdot t^{23}-\frac{683648951099121865}{1298074214633706907132624082305024}\cdot t^{21}+\frac{63468735513181075}{5192296858534827628530496329220096}\cdot t^{19}-\frac{2388983881301775}{10384593717069655257060992658440192}\cdot t^{17}+\frac{142500792919755}{41538374868278621028243970633760768}\cdot t^{15}-\frac{3270510001437}{83076749736557242056487941267521536}\cdot t^{13}+\frac{111203042769}{332306998946228968225951765070086144}\cdot t^{11}-\frac{1329890705}{664613997892457936451903530140172288}\cdot t^9+\frac{1329890705}{170141183460469231731687303715884105728}\cdot t^7-\frac{6051507}{340282366920938463463374607431768211456}\cdot t^5+\frac{26197}{1361129467683753853853498429727072845824}\cdot t^3-\frac{17}{2722258935367507707706996859454145691648}\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.