Rule: Q[1, 72, 74]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{73}-36\cdot t^{71}+\frac{2485}{8}\cdot t^{69}-\frac{13685}{8}\cdot t^{67}+\frac{864501}{128}\cdot t^{65}-\frac{162877}{8}\cdot t^{63}+\frac{6237231}{128}\cdot t^{61}-\frac{12168585}{128}\cdot t^{59}+\frac{630922695}{4096}\cdot t^{57}-\frac{430321633}{2048}\cdot t^{55}+\frac{127805525001}{524288}\cdot t^{53}-\frac{127067830773}{524288}\cdot t^{51}+\frac{1742058970275}{8388608}\cdot t^{49}-\frac{322928964225}{2097152}\cdot t^{47}+\frac{3324630574545}{33554432}\cdot t^{45}-\frac{1859539134915}{33554432}\cdot t^{43}+\frac{57902201338905}{2147483648}\cdot t^{41}-\frac{12249691717725}{1073741824}\cdot t^{39}+\frac{144079707346575}{34359738368}\cdot t^{37}-\frac{45912480905655}{34359738368}\cdot t^{35}+\frac{202355008436035}{549755813888}\cdot t^{33}-\frac{5999744185435}{68719476736}\cdot t^{31}+\frac{19509657665925}{1099511627776}\cdot t^{29}-\frac{3376351667675}{1099511627776}\cdot t^{27}+\frac{15801325804719}{35184372088832}\cdot t^{25}-\frac{967428110493}{17592186044416}\cdot t^{23}+\frac{6275879793711}{1125899906842624}\cdot t^{21}-\frac{519280833995}{1125899906842624}\cdot t^{19}+\frac{551534301945}{18014398509481984}\cdot t^{17}-\frac{7184738033}{4503599627370496}\cdot t^{15}+\frac{4572106021}{72057594037927936}\cdot t^{13}-\frac{133767543}{72057594037927936}\cdot t^{11}+\frac{350343565}{9223372036854775808}\cdot t^9-\frac{2330445}{4611686018427387904}\cdot t^7+\frac{575757}{147573952589676412928}\cdot t^5-\frac{2109}{147573952589676412928}\cdot t^3+\frac{37}{2361183241434822606848}\cdot t$
• $P_3$:
  $2\cdot t^{147}-73\cdot t^{145}+1305\cdot t^{143}-\frac{30459}{2}\cdot t^{141}+\frac{16701685}{128}\cdot t^{139}-\frac{224036169}{256}\cdot t^{137}+\frac{2449672477}{512}\cdot t^{135}-\frac{22449126195}{1024}\cdot t^{133}+\frac{2815120424853}{32768}\cdot t^{131}-\frac{19161271317045}{65536}\cdot t^{129}+\frac{7164649275069}{8192}\cdot t^{127}-\frac{38038725182367}{16384}\cdot t^{125}+\frac{2890197256503375}{524288}\cdot t^{123}-\frac{12356210835068275}{1048576}\cdot t^{121}+\frac{47817745555754625}{2097152}\cdot t^{119}-\frac{168284908043585575}{4194304}\cdot t^{117}+\frac{17302748272481389575}{268435456}\cdot t^{115}-\frac{50929283756675127375}{536870912}\cdot t^{113}+\frac{68863356327401753425}{536870912}\cdot t^{111}-\frac{171526230264703265875}{1073741824}\cdot t^{109}+\frac{100960339133804342294025}{549755813888}\cdot t^{107}-\frac{214677946467118269647325}{1099511627776}\cdot t^{105}+\frac{422850500617051137184125}{2199023255552}\cdot t^{103}-\frac{772603019040476390827203}{4398046511104}\cdot t^{101}+\frac{20976587344916160073534275}{140737488355328}\cdot t^{99}-\frac{33091845596809200818443827}{281474976710656}\cdot t^{97}+\frac{12143413705764788698823649}{140737488355328}\cdot t^{95}-\frac{16596370430437643569099355}{281474976710656}\cdot t^{93}+\frac{338091774768629710421938289}{9007199254740992}\cdot t^{91}-\frac{401183951804560609729886205}{18014398509481984}\cdot t^{89}+\frac{443795580583802075622100107}{36028797018963968}\cdot t^{87}-\frac{457744490478082041605259581}{72057594037927936}\cdot t^{85}+\frac{28174962603564704974668563865}{9223372036854775808}\cdot t^{83}-\frac{25264663436081868518787120641}{18446744073709551616}\cdot t^{81}+\frac{10559534253470750000112264045}{18446744073709551616}\cdot t^{79}-\frac{8226024029062801706787834519}{36893488147419103232}\cdot t^{77}+\frac{191026558008236172968739712719}{2361183241434822606848}\cdot t^{75}-\frac{129071998654213630384283589675}{4722366482869645213696}\cdot t^{73}+\frac{81148615421835746566961070255}{9444732965739290427392}\cdot t^{71}-\frac{47436911155789656602893027425}{18889465931478580854784}\cdot t^{69}+\frac{412174050264750127371803860515}{604462909807314587353088}\cdot t^{67}-\frac{207731211564933332942570853795}{1208925819614629174706176}\cdot t^{65}+\frac{12131652068032943972387336475}{302231454903657293676544}\cdot t^{63}-\frac{5247644848032854834567545545}{604462909807314587353088}\cdot t^{61}+\frac{33577587663986448766638490725}{19342813113834066795298816}\cdot t^{59}-\frac{12395092231516896189799019985}{38685626227668133590597632}\cdot t^{57}+\frac{4216233418904724279394551555}{77371252455336267181195264}\cdot t^{55}-\frac{1318960738797875617211061525}{154742504910672534362390528}\cdot t^{53}+\frac{12116852653756484003445618543}{9903520314283042199192993792}\cdot t^{51}-\frac{3184701532372607112841303575}{19807040628566084398385987584}\cdot t^{49}+\frac{382164183884712853540956429}{19807040628566084398385987584}\cdot t^{47}-\frac{83509092941050049459828967}{39614081257132168796771975168}\cdot t^{45}+\frac{1059923102713327550836290735}{5070602400912917605986812821504}\cdot t^{43}-\frac{190091472045707006634591963}{10141204801825835211973625643008}\cdot t^{41}+\frac{30708236224877806430332035}{20282409603651670423947251286016}\cdot t^{39}-\frac{4448641846067342045919069}{40564819207303340847894502572032}\cdot t^{37}+\frac{9201228166089595660192857}{1298074214633706907132624082305024}\cdot t^{35}-\frac{1055471517027821364529545}{2596148429267413814265248164610048}\cdot t^{33}+\frac{26690084338634563240977}{1298074214633706907132624082305024}\cdot t^{31}-\frac{2363528702621419140555}{2596148429267413814265248164610048}\cdot t^{29}+\frac{2907856525043321730501}{83076749736557242056487941267521536}\cdot t^{27}-\frac{192322901882458248993}{166153499473114484112975882535043072}\cdot t^{25}+\frac{10820868448000276575}{332306998946228968225951765070086144}\cdot t^{23}-\frac{511238042454541545}{664613997892457936451903530140172288}\cdot t^{21}+\frac{2556190212272707725}{170141183460469231731687303715884105728}\cdot t^{19}-\frac{81021042872777205}{340282366920938463463374607431768211456}\cdot t^{17}+\frac{1018002755977245}{340282366920938463463374607431768211456}\cdot t^{15}-\frac{19696017943175}{680564733841876926926749214863536422912}\cdot t^{13}+\frac{9036996468045}{43556142965880123323311949751266331066368}\cdot t^{11}-\frac{91182316225}{87112285931760246646623899502532662132736}\cdot t^9+\frac{601202085}{174224571863520493293247799005065324265472}\cdot t^7-\frac{2309355}{348449143727040986586495598010130648530944}\cdot t^5+\frac{67525}{11150372599265311570767859136324180752990208}\cdot t^3-\frac{37}{22300745198530623141535718272648361505980416}\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.