Rule: Q[1, 68, 70]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{69}-34\cdot t^{67}+\frac{2211}{8}\cdot t^{65}-1430\cdot t^{63}+\frac{42315}{8}\cdot t^{61}-\frac{119133}{8}\cdot t^{59}+\frac{67945521}{2048}\cdot t^{57}-\frac{61474519}{1024}\cdot t^{55}+\frac{2944827765}{32768}\cdot t^{53}-\frac{3695785665}{32768}\cdot t^{51}+\frac{62828356305}{524288}\cdot t^{49}-\frac{14230767915}{131072}\cdot t^{47}+\frac{176821380645}{2097152}\cdot t^{45}-\frac{118119545775}{2097152}\cdot t^{43}+\frac{2176774486425}{67108864}\cdot t^{41}-\frac{540895478445}{33554432}\cdot t^{39}+\frac{14844575908435}{2147483648}\cdot t^{37}-\frac{5486397089355}{2147483648}\cdot t^{35}+\frac{27900908274925}{34359738368}\cdot t^{33}-\frac{950185730725}{4294967296}\cdot t^{31}+\frac{3534690918297}{68719476736}\cdot t^{29}-\frac{697319977079}{68719476736}\cdot t^{27}+\frac{7416948847113}{4398046511104}\cdot t^{25}-\frac{514589420475}{2199023255552}\cdot t^{23}+\frac{1886827875075}{70368744177664}\cdot t^{21}-\frac{176103935007}{70368744177664}\cdot t^{19}+\frac{210585824379}{1125899906842624}\cdot t^{17}-\frac{3083513363}{281474976710656}\cdot t^{15}+\frac{2202509545}{4503599627370496}\cdot t^{13}-\frac{72243795}{4503599627370496}\cdot t^{11}+\frac{52978783}{144115188075855872}\cdot t^9-\frac{394383}{72057594037927936}\cdot t^7+\frac{435897}{9223372036854775808}\cdot t^5-\frac{1785}{9223372036854775808}\cdot t^3+\frac{35}{147573952589676412928}\cdot t$
• $P_3$:
  $2\cdot t^{139}-69\cdot t^{137}+\frac{2329}{2}\cdot t^{135}-\frac{51255}{4}\cdot t^{133}+\frac{13232835}{128}\cdot t^{131}-\frac{166929763}{256}\cdot t^{129}+\frac{107134027}{32}\cdot t^{127}-\frac{920708217}{64}\cdot t^{125}+\frac{108113464875}{2048}\cdot t^{123}-\frac{688019785375}{4096}\cdot t^{121}+\frac{3842325878325}{8192}\cdot t^{119}-\frac{19011254398675}{16384}\cdot t^{117}+\frac{21501728724901425}{8388608}\cdot t^{115}-\frac{85368765470459625}{16777216}\cdot t^{113}+\frac{153121753939078375}{16777216}\cdot t^{111}-\frac{498564430825639189}{33554432}\cdot t^{109}+\frac{47331455481285681717}{2147483648}\cdot t^{107}-\frac{128367615511416117177}{4294967296}\cdot t^{105}+\frac{319165382828930783145}{8589934592}\cdot t^{103}-\frac{729263051761797913815}{17179869184}\cdot t^{101}+\frac{24551856075980529765105}{549755813888}\cdot t^{99}-\frac{47659485323962204838145}{1099511627776}\cdot t^{97}+\frac{21369661370220341460555}{549755813888}\cdot t^{95}-\frac{35457279085111045938825}{1099511627776}\cdot t^{93}+\frac{871759999575316405323525}{35184372088832}\cdot t^{91}-\frac{1241689460264668062539073}{70368744177664}\cdot t^{89}+\frac{1640504698514318533368087}{140737488355328}\cdot t^{87}-\frac{2011513627381863531081617}{281474976710656}\cdot t^{85}+\frac{73276567854625028632258905}{18014398509481984}\cdot t^{83}-\frac{77465101090179860961657985}{36028797018963968}\cdot t^{81}+\frac{38028322353361022653904829}{36028797018963968}\cdot t^{79}-\frac{34674537191685501863474631}{72057594037927936}\cdot t^{77}+\frac{1878846218942069971343088339}{9223372036854775808}\cdot t^{75}-\frac{1476578379372484896764958975}{18446744073709551616}\cdot t^{73}+\frac{1076705877078493426386879075}{36893488147419103232}\cdot t^{71}-\frac{728058259738790793080651565}{73786976294838206464}\cdot t^{69}+\frac{7299250757894030771654737485}{2361183241434822606848}\cdot t^{67}-\frac{4234752932485883504625721485}{4722366482869645213696}\cdot t^{65}+\frac{284064954191519533334026725}{1180591620717411303424}\cdot t^{63}-\frac{140842562969291101447411575}{2361183241434822606848}\cdot t^{61}+\frac{1030967560935210862595052729}{75557863725914323419136}\cdot t^{59}-\frac{434586227336818375437333141}{151115727451828646838272}\cdot t^{57}+\frac{168513026926521410883863871}{302231454903657293676544}\cdot t^{55}-\frac{59995647323395899103940985}{604462909807314587353088}\cdot t^{53}+\frac{1252636394115750741897434505}{77371252455336267181195264}\cdot t^{51}-\frac{373593310525750221267655905}{154742504910672534362390528}\cdot t^{49}+\frac{50803160635786570329644235}{154742504910672534362390528}\cdot t^{47}-\frac{12564222522828936748191585}{309485009821345068724781056}\cdot t^{45}+\frac{90134639837685850584852675}{19807040628566084398385987584}\cdot t^{43}-\frac{18253325807003884969302975}{39614081257132168796771975168}\cdot t^{41}+\frac{3326161591498485705517431}{79228162514264337593543950336}\cdot t^{39}-\frac{543001925380122914251689}{158456325028528675187087900672}\cdot t^{37}+\frac{1264473015046020492628059}{5070602400912917605986812821504}\cdot t^{35}-\frac{163166654511468703776555}{10141204801825835211973625643008}\cdot t^{33}+\frac{4637811885338903724915}{5070602400912917605986812821504}\cdot t^{31}-\frac{461301075226222509537}{10141204801825835211973625643008}\cdot t^{29}+\frac{637034818169545370313}{324518553658426726783156020576256}\cdot t^{27}-\frac{47262570530016999573}{649037107316853453566312041152512}\cdot t^{25}+\frac{2981238679353469275}{1298074214633706907132624082305024}\cdot t^{23}-\frac{157826613491614925}{2596148429267413814265248164610048}\cdot t^{21}+\frac{220957258888260895}{166153499473114484112975882535043072}\cdot t^{19}-\frac{7840566771092055}{332306998946228968225951765070086144}\cdot t^{17}+\frac{110247837145215}{332306998946228968225951765070086144}\cdot t^{15}-\frac{2386316821325}{664613997892457936451903530140172288}\cdot t^{13}+\frac{4898229264825}{170141183460469231731687303715884105728}\cdot t^{11}-\frac{55262073757}{340282366920938463463374607431768211456}\cdot t^9+\frac{407337153}{680564733841876926926749214863536422912}\cdot t^7-\frac{1748943}{1361129467683753853853498429727072845824}\cdot t^5+\frac{57155}{43556142965880123323311949751266331066368}\cdot t^3-\frac{35}{87112285931760246646623899502532662132736}\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.