Rule: Q[16, 17, 34, 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.

• $P_1$:
  $65536\cdot t^{16}-245760\cdot t^{14}+372736\cdot t^{12}-292864\cdot t^{10}+126720\cdot t^8-29568\cdot t^6+3360\cdot t^4-144\cdot t^2+1$
• $P_2$:
  $65536\cdot t^{33}-524288\cdot t^{31}+1904640\cdot t^{29}-4157440\cdot t^{27}+6080256\cdot t^{25}-6289920\cdot t^{23}+4736160\cdot t^{21}-2631200\cdot t^{19}+1081575\cdot t^{17}-326876\cdot t^{15}+\frac{572033}{8}\cdot t^{13}-\frac{88179}{8}\cdot t^{11}+\frac{146965}{128}\cdot t^9-\frac{4845}{64}\cdot t^7+\frac{2907}{1024}\cdot t^5-\frac{51}{1024}\cdot t^3+\frac{17}{65536}\cdot t$
• $P_3$:
  $65536\cdot t^{67}-1081344\cdot t^{65}+8519680\cdot t^{63}-42663936\cdot t^{61}+152490240\cdot t^{59}-414144128\cdot t^{57}+888405952\cdot t^{55}-1544827680\cdot t^{53}+2217471399\cdot t^{51}-\frac{5324436975}{2}\cdot t^{49}+\frac{5397877485}{2}\cdot t^{47}-\frac{9306388455}{4}\cdot t^{45}+\frac{219364870725}{128}\cdot t^{43}-\frac{277044025545}{256}\cdot t^{41}+\frac{300497488025}{512}\cdot t^{39}-\frac{280086337895}{1024}\cdot t^{37}+\frac{7174519270695}{65536}\cdot t^{35}-\frac{4923689695575}{131072}\cdot t^{33}+\frac{722141155351}{65536}\cdot t^{31}-\frac{360682746765}{131072}\cdot t^{29}+\frac{4881239839553}{8388608}\cdot t^{27}-\frac{1735881645069}{16777216}\cdot t^{25}+\frac{514589420475}{33554432}\cdot t^{23}-\frac{125788525005}{67108864}\cdot t^{21}+\frac{400236215925}{2147483648}\cdot t^{19}-\frac{63665481789}{4294967296}\cdot t^{17}+\frac{3964517181}{4294967296}\cdot t^{15}-\frac{376038215}{8589934592}\cdot t^{13}+\frac{419014011}{274877906944}\cdot t^{11}-\frac{20376455}{549755813888}\cdot t^9+\frac{643467}{1099511627776}\cdot t^7-\frac{11781}{2199023255552}\cdot t^5+\frac{6545}{281474976710656}\cdot t^3-\frac{17}{562949953421312}\cdot t$
• $P_4$:
  $65536\cdot t^{135}-2195456\cdot t^{133}+35954688\cdot t^{131}-383651840\cdot t^{129}+2999459840\cdot t^{127}-18319601664\cdot t^{125}+91010841600\cdot t^{123}-378103180800\cdot t^{121}+1340346236625\cdot t^{119}-\frac{8233220408875}{2}\cdot t^{117}+\frac{88683545547025}{8}\cdot t^{115}-\frac{422778648044181}{16}\cdot t^{113}+\frac{3595891511859647}{64}\cdot t^{111}-\frac{13729154271359065}{128}\cdot t^{109}+\frac{94625060938196085}{512}\cdot t^{107}-\frac{295657697289537189}{1024}\cdot t^{105}+\frac{26904850453347884199}{65536}\cdot t^{103}-\frac{69862174706592405189}{131072}\cdot t^{101}+\frac{332207139612327350475}{524288}\cdot t^{99}-\frac{724937847170220412575}{1048576}\cdot t^{97}+\frac{1454875265700235448685}{2097152}\cdot t^{95}-\frac{2689862551284286243635}{4194304}\cdot t^{93}+\frac{9176421048161225319195}{16777216}\cdot t^{91}-\frac{14458424083193619731475}{33554432}\cdot t^{89}+\frac{674037960830788272243525}{2147483648}\cdot t^{87}-\frac{908676040168641054581271}{4294967296}\cdot t^{85}+\frac{2268512911469964031367229}{17179869184}\cdot t^{83}-\frac{2623088493962720896616609}{34359738368}\cdot t^{81}+\frac{5620903915634401921321305}{137438953472}\cdot t^{79}-\frac{5581052195961840902220735}{274877906944}\cdot t^{77}+\frac{10270540078858079547105579}{1099511627776}\cdot t^{75}-\frac{8755990389809883484859595}{2199023255552}\cdot t^{73}+\frac{442514283546545649965596455}{281474976710656}\cdot t^{71}-\frac{323521034013876416641514325}{562949953421312}\cdot t^{69}+\frac{437704928371715151926754675}{2251799813685248}\cdot t^{67}-\frac{273766788296990721615291255}{4503599627370496}\cdot t^{65}+\frac{79088183285797319577750807}{4503599627370496}\cdot t^{63}-\frac{42167409761715032796982617}{9007199254740992}\cdot t^{61}+\frac{41442728176121648774692905}{36028797018963968}\cdot t^{59}-\frac{18743988345055284444488385}{72057594037927936}\cdot t^{57}+\frac{498590089978470566223391041}{9223372036854775808}\cdot t^{55}-\frac{190091472045707006634591963}{18446744073709551616}\cdot t^{53}+\frac{132698099533426674337622961}{73786976294838206464}\cdot t^{51}-\frac{42308096250342338029624725}{147573952589676412928}\cdot t^{49}+\frac{24582174501187050159505275}{590295810358705651712}\cdot t^{47}-\frac{6489213830472088210604445}{1180591620717411303424}\cdot t^{45}+\frac{3103537049356216100723865}{4722366482869645213696}\cdot t^{43}-\frac{669972258084786789135465}{9444732965739290427392}\cdot t^{41}+\frac{4161948875981251265841525}{604462909807314587353088}\cdot t^{39}-\frac{723435167042483506448175}{1208925819614629174706176}\cdot t^{37}+\frac{224096661046648379206737}{4835703278458516698824704}\cdot t^{35}-\frac{30758365241696836361709}{9671406556917033397649408}\cdot t^{33}+\frac{3718044150095221977789}{19342813113834066795298816}\cdot t^{31}-\frac{393018988359690434115}{38685626227668133590597632}\cdot t^{29}+\frac{72071232734432843835}{154742504910672534362390528}\cdot t^{27}-\frac{5678339548773496787}{309485009821345068724781056}\cdot t^{25}+\frac{12167870461657493115}{19807040628566084398385987584}\cdot t^{23}-\frac{683648951099121865}{39614081257132168796771975168}\cdot t^{21}+\frac{63468735513181075}{158456325028528675187087900672}\cdot t^{19}-\frac{2388983881301775}{316912650057057350374175801344}\cdot t^{17}+\frac{142500792919755}{1267650600228229401496703205376}\cdot t^{15}-\frac{3270510001437}{2535301200456458802993406410752}\cdot t^{13}+\frac{111203042769}{10141204801825835211973625643008}\cdot t^{11}-\frac{1329890705}{20282409603651670423947251286016}\cdot t^9+\frac{1329890705}{5192296858534827628530496329220096}\cdot t^7-\frac{6051507}{10384593717069655257060992658440192}\cdot t^5+\frac{26197}{41538374868278621028243970633760768}\cdot t^3-\frac{17}{83076749736557242056487941267521536}\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.