Rule: Q[36, 37, 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.

• $P_1$:
  $68719476736\cdot t^{36}-601295421440\cdot t^{34}+2409476653056\cdot t^{32}-5858335391744\cdot t^{30}+9652938997760\cdot t^{28}-11402534191104\cdot t^{26}+9961891430400\cdot t^{24}-6546385797120\cdot t^{22}+3259084308480\cdot t^{20}-1228623052800\cdot t^{18}+348109864960\cdot t^{16}-73030041600\cdot t^{14}+11076222976\cdot t^{12}-1171523584\cdot t^{10}+81861120\cdot t^8-3472896\cdot t^6+77520\cdot t^4-684\cdot t^2+1$
• $P_2$:
  $68719476736\cdot t^{73}-1236950581248\cdot t^{71}+10672993730560\cdot t^{69}-58776627445760\cdot t^{67}+232062720147456\cdot t^{65}-699551388270592\cdot t^{63}+1674293947662336\cdot t^{61}-3266479663349760\cdot t^{59}+5292563166658560\cdot t^{57}-7219598986313728\cdot t^{55}+8375862886465536\cdot t^{53}-8327517357539328\cdot t^{51}+7135473542246400\cdot t^{49}-5290868149862400\cdot t^{47}+3404421708334080\cdot t^{45}-1904168074152960\cdot t^{43}+926435221422480\cdot t^{41}-391990134967200\cdot t^{39}+144079707346575\cdot t^{37}-45912480905655\cdot t^{35}+\frac{202355008436035}{16}\cdot t^{33}-\frac{5999744185435}{2}\cdot t^{31}+\frac{19509657665925}{32}\cdot t^{29}-\frac{3376351667675}{32}\cdot t^{27}+\frac{15801325804719}{1024}\cdot t^{25}-\frac{967428110493}{512}\cdot t^{23}+\frac{6275879793711}{32768}\cdot t^{21}-\frac{519280833995}{32768}\cdot t^{19}+\frac{551534301945}{524288}\cdot t^{17}-\frac{7184738033}{131072}\cdot t^{15}+\frac{4572106021}{2097152}\cdot t^{13}-\frac{133767543}{2097152}\cdot t^{11}+\frac{350343565}{268435456}\cdot t^9-\frac{2330445}{134217728}\cdot t^7+\frac{575757}{4294967296}\cdot t^5-\frac{2109}{4294967296}\cdot t^3+\frac{37}{68719476736}\cdot t$
• $P_3$:
  $68719476736\cdot t^{147}-2508260900864\cdot t^{145}+44839458570240\cdot t^{143}-523281635475456\cdot t^{141}+4483324428943360\cdot t^{139}-30069625593004032\cdot t^{137}+164394737103536128\cdot t^{135}-753267678369546240\cdot t^{133}+2951867714610659328\cdot t^{131}-10046024616270888960\cdot t^{129}+30050717113019006976\cdot t^{127}-79772988593651318784\cdot t^{125}+189411967402205184000\cdot t^{123}-404888316643517235200\cdot t^{121}+783445943185483776000\cdot t^{119}-1378589966693053030400\cdot t^{117}+2214751778877617865600\cdot t^{115}-3259474160427208152000\cdot t^{113}+4407254804953712219200\cdot t^{111}-5488839368470504508000\cdot t^{109}+\frac{100960339133804342294025}{16}\cdot t^{107}-\frac{214677946467118269647325}{32}\cdot t^{105}+\frac{422850500617051137184125}{64}\cdot t^{103}-\frac{772603019040476390827203}{128}\cdot t^{101}+\frac{20976587344916160073534275}{4096}\cdot t^{99}-\frac{33091845596809200818443827}{8192}\cdot t^{97}+\frac{12143413705764788698823649}{4096}\cdot t^{95}-\frac{16596370430437643569099355}{8192}\cdot t^{93}+\frac{338091774768629710421938289}{262144}\cdot t^{91}-\frac{401183951804560609729886205}{524288}\cdot t^{89}+\frac{443795580583802075622100107}{1048576}\cdot t^{87}-\frac{457744490478082041605259581}{2097152}\cdot t^{85}+\frac{28174962603564704974668563865}{268435456}\cdot t^{83}-\frac{25264663436081868518787120641}{536870912}\cdot t^{81}+\frac{10559534253470750000112264045}{536870912}\cdot t^{79}-\frac{8226024029062801706787834519}{1073741824}\cdot t^{77}+\frac{191026558008236172968739712719}{68719476736}\cdot t^{75}-\frac{129071998654213630384283589675}{137438953472}\cdot t^{73}+\frac{81148615421835746566961070255}{274877906944}\cdot t^{71}-\frac{47436911155789656602893027425}{549755813888}\cdot t^{69}+\frac{412174050264750127371803860515}{17592186044416}\cdot t^{67}-\frac{207731211564933332942570853795}{35184372088832}\cdot t^{65}+\frac{12131652068032943972387336475}{8796093022208}\cdot t^{63}-\frac{5247644848032854834567545545}{17592186044416}\cdot t^{61}+\frac{33577587663986448766638490725}{562949953421312}\cdot t^{59}-\frac{12395092231516896189799019985}{1125899906842624}\cdot t^{57}+\frac{4216233418904724279394551555}{2251799813685248}\cdot t^{55}-\frac{1318960738797875617211061525}{4503599627370496}\cdot t^{53}+\frac{12116852653756484003445618543}{288230376151711744}\cdot t^{51}-\frac{3184701532372607112841303575}{576460752303423488}\cdot t^{49}+\frac{382164183884712853540956429}{576460752303423488}\cdot t^{47}-\frac{83509092941050049459828967}{1152921504606846976}\cdot t^{45}+\frac{1059923102713327550836290735}{147573952589676412928}\cdot t^{43}-\frac{190091472045707006634591963}{295147905179352825856}\cdot t^{41}+\frac{30708236224877806430332035}{590295810358705651712}\cdot t^{39}-\frac{4448641846067342045919069}{1180591620717411303424}\cdot t^{37}+\frac{9201228166089595660192857}{37778931862957161709568}\cdot t^{35}-\frac{1055471517027821364529545}{75557863725914323419136}\cdot t^{33}+\frac{26690084338634563240977}{37778931862957161709568}\cdot t^{31}-\frac{2363528702621419140555}{75557863725914323419136}\cdot t^{29}+\frac{2907856525043321730501}{2417851639229258349412352}\cdot t^{27}-\frac{192322901882458248993}{4835703278458516698824704}\cdot t^{25}+\frac{10820868448000276575}{9671406556917033397649408}\cdot t^{23}-\frac{511238042454541545}{19342813113834066795298816}\cdot t^{21}+\frac{2556190212272707725}{4951760157141521099596496896}\cdot t^{19}-\frac{81021042872777205}{9903520314283042199192993792}\cdot t^{17}+\frac{1018002755977245}{9903520314283042199192993792}\cdot t^{15}-\frac{19696017943175}{19807040628566084398385987584}\cdot t^{13}+\frac{9036996468045}{1267650600228229401496703205376}\cdot t^{11}-\frac{91182316225}{2535301200456458802993406410752}\cdot t^9+\frac{601202085}{5070602400912917605986812821504}\cdot t^7-\frac{2309355}{10141204801825835211973625643008}\cdot t^5+\frac{67525}{324518553658426726783156020576256}\cdot t^3-\frac{37}{649037107316853453566312041152512}\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.