Rule: Q[6, 63, 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.

• $P_1$:
  $64\cdot t^6-80\cdot t^4+24\cdot t^2-1$
• $P_2$:
  $64\cdot t^{69}-1088\cdot t^{67}+8844\cdot t^{65}-45760\cdot t^{63}+169260\cdot t^{61}-476532\cdot t^{59}+\frac{67945521}{64}\cdot t^{57}-\frac{61474519}{32}\cdot t^{55}+\frac{2944827765}{1024}\cdot t^{53}-\frac{3695785665}{1024}\cdot t^{51}+\frac{62828356305}{16384}\cdot t^{49}-\frac{14230767915}{4096}\cdot t^{47}+\frac{176821380645}{65536}\cdot t^{45}-\frac{118119545775}{65536}\cdot t^{43}+\frac{2176774486425}{2097152}\cdot t^{41}-\frac{540895478445}{1048576}\cdot t^{39}+\frac{14844575908435}{67108864}\cdot t^{37}-\frac{5486397089355}{67108864}\cdot t^{35}+\frac{27900908274925}{1073741824}\cdot t^{33}-\frac{950185730725}{134217728}\cdot t^{31}+\frac{3534690918297}{2147483648}\cdot t^{29}-\frac{697319977079}{2147483648}\cdot t^{27}+\frac{7416948847113}{137438953472}\cdot t^{25}-\frac{514589420475}{68719476736}\cdot t^{23}+\frac{1886827875075}{2199023255552}\cdot t^{21}-\frac{176103935007}{2199023255552}\cdot t^{19}+\frac{210585824379}{35184372088832}\cdot t^{17}-\frac{3083513363}{8796093022208}\cdot t^{15}+\frac{2202509545}{140737488355328}\cdot t^{13}-\frac{72243795}{140737488355328}\cdot t^{11}+\frac{52978783}{4503599627370496}\cdot t^9-\frac{394383}{2251799813685248}\cdot t^7+\frac{435897}{288230376151711744}\cdot t^5-\frac{1785}{288230376151711744}\cdot t^3+\frac{35}{4611686018427387904}\cdot t$
• $P_3$:
  $64\cdot t^{139}-2208\cdot t^{137}+37264\cdot t^{135}-410040\cdot t^{133}+\frac{13232835}{4}\cdot t^{131}-\frac{166929763}{8}\cdot t^{129}+107134027\cdot t^{127}-\frac{920708217}{2}\cdot t^{125}+\frac{108113464875}{64}\cdot t^{123}-\frac{688019785375}{128}\cdot t^{121}+\frac{3842325878325}{256}\cdot t^{119}-\frac{19011254398675}{512}\cdot t^{117}+\frac{21501728724901425}{262144}\cdot t^{115}-\frac{85368765470459625}{524288}\cdot t^{113}+\frac{153121753939078375}{524288}\cdot t^{111}-\frac{498564430825639189}{1048576}\cdot t^{109}+\frac{47331455481285681717}{67108864}\cdot t^{107}-\frac{128367615511416117177}{134217728}\cdot t^{105}+\frac{319165382828930783145}{268435456}\cdot t^{103}-\frac{729263051761797913815}{536870912}\cdot t^{101}+\frac{24551856075980529765105}{17179869184}\cdot t^{99}-\frac{47659485323962204838145}{34359738368}\cdot t^{97}+\frac{21369661370220341460555}{17179869184}\cdot t^{95}-\frac{35457279085111045938825}{34359738368}\cdot t^{93}+\frac{871759999575316405323525}{1099511627776}\cdot t^{91}-\frac{1241689460264668062539073}{2199023255552}\cdot t^{89}+\frac{1640504698514318533368087}{4398046511104}\cdot t^{87}-\frac{2011513627381863531081617}{8796093022208}\cdot t^{85}+\frac{73276567854625028632258905}{562949953421312}\cdot t^{83}-\frac{77465101090179860961657985}{1125899906842624}\cdot t^{81}+\frac{38028322353361022653904829}{1125899906842624}\cdot t^{79}-\frac{34674537191685501863474631}{2251799813685248}\cdot t^{77}+\frac{1878846218942069971343088339}{288230376151711744}\cdot t^{75}-\frac{1476578379372484896764958975}{576460752303423488}\cdot t^{73}+\frac{1076705877078493426386879075}{1152921504606846976}\cdot t^{71}-\frac{728058259738790793080651565}{2305843009213693952}\cdot t^{69}+\frac{7299250757894030771654737485}{73786976294838206464}\cdot t^{67}-\frac{4234752932485883504625721485}{147573952589676412928}\cdot t^{65}+\frac{284064954191519533334026725}{36893488147419103232}\cdot t^{63}-\frac{140842562969291101447411575}{73786976294838206464}\cdot t^{61}+\frac{1030967560935210862595052729}{2361183241434822606848}\cdot t^{59}-\frac{434586227336818375437333141}{4722366482869645213696}\cdot t^{57}+\frac{168513026926521410883863871}{9444732965739290427392}\cdot t^{55}-\frac{59995647323395899103940985}{18889465931478580854784}\cdot t^{53}+\frac{1252636394115750741897434505}{2417851639229258349412352}\cdot t^{51}-\frac{373593310525750221267655905}{4835703278458516698824704}\cdot t^{49}+\frac{50803160635786570329644235}{4835703278458516698824704}\cdot t^{47}-\frac{12564222522828936748191585}{9671406556917033397649408}\cdot t^{45}+\frac{90134639837685850584852675}{618970019642690137449562112}\cdot t^{43}-\frac{18253325807003884969302975}{1237940039285380274899124224}\cdot t^{41}+\frac{3326161591498485705517431}{2475880078570760549798248448}\cdot t^{39}-\frac{543001925380122914251689}{4951760157141521099596496896}\cdot t^{37}+\frac{1264473015046020492628059}{158456325028528675187087900672}\cdot t^{35}-\frac{163166654511468703776555}{316912650057057350374175801344}\cdot t^{33}+\frac{4637811885338903724915}{158456325028528675187087900672}\cdot t^{31}-\frac{461301075226222509537}{316912650057057350374175801344}\cdot t^{29}+\frac{637034818169545370313}{10141204801825835211973625643008}\cdot t^{27}-\frac{47262570530016999573}{20282409603651670423947251286016}\cdot t^{25}+\frac{2981238679353469275}{40564819207303340847894502572032}\cdot t^{23}-\frac{157826613491614925}{81129638414606681695789005144064}\cdot t^{21}+\frac{220957258888260895}{5192296858534827628530496329220096}\cdot t^{19}-\frac{7840566771092055}{10384593717069655257060992658440192}\cdot t^{17}+\frac{110247837145215}{10384593717069655257060992658440192}\cdot t^{15}-\frac{2386316821325}{20769187434139310514121985316880384}\cdot t^{13}+\frac{4898229264825}{5316911983139663491615228241121378304}\cdot t^{11}-\frac{55262073757}{10633823966279326983230456482242756608}\cdot t^9+\frac{407337153}{21267647932558653966460912964485513216}\cdot t^7-\frac{1748943}{42535295865117307932921825928971026432}\cdot t^5+\frac{57155}{1361129467683753853853498429727072845824}\cdot t^3-\frac{35}{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.