Rule: Q[19, 20, 76]

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.

• $P_1$:
  $262144\cdot t^{19}-1245184\cdot t^{17}+2490368\cdot t^{15}-2723840\cdot t^{13}+1770496\cdot t^{11}-695552\cdot t^9+160512\cdot t^7-20064\cdot t^5+1140\cdot t^3-19\cdot t$
• $P_2$:
  $262144\cdot t^{39}-2621440\cdot t^{37}+12107776\cdot t^{35}-34258944\cdot t^{33}+66412544\cdot t^{31}-93454336\cdot t^{29}+98674240\cdot t^{27}-79694784\cdot t^{25}+49741380\cdot t^{23}-24075480\cdot t^{21}+\frac{36063885}{4}\cdot t^{19}-\frac{10367825}{4}\cdot t^{17}+\frac{9026235}{16}\cdot t^{15}-\frac{364021}{4}\cdot t^{13}+\frac{5400883}{512}\cdot t^{11}-\frac{429913}{512}\cdot t^9+\frac{702525}{16384}\cdot t^7-\frac{10317}{8192}\cdot t^5+\frac{4579}{262144}\cdot t^3-\frac{19}{262144}\cdot t$
• $P_3$:
  $262144\cdot t^{115}-7602176\cdot t^{113}+107364352\cdot t^{111}-984023040\cdot t^{109}+6580767744\cdot t^{107}-34232878080\cdot t^{105}+144199828864\cdot t^{103}-505584804608\cdot t^{101}+1505196546100\cdot t^{99}-3862747708820\cdot t^{97}+8645291278855\cdot t^{95}-17032359991640\cdot t^{93}+\frac{476165369302455}{16}\cdot t^{91}-\frac{742421620175025}{16}\cdot t^{89}+\frac{8305367587711887}{128}\cdot t^{87}-\frac{5229904048702417}{64}\cdot t^{85}+\frac{761955208081136017}{8192}\cdot t^{83}-\frac{786093705107531429}{8192}\cdot t^{81}+\frac{23579204115729273255}{262144}\cdot t^{79}-\frac{5030222617592427411}{65536}\cdot t^{77}+\frac{250488161312164424649}{4194304}\cdot t^{75}-\frac{177930947569645213515}{4194304}\cdot t^{73}+\frac{923974240513201680465}{33554432}\cdot t^{71}-\frac{274214587857330809925}{16777216}\cdot t^{69}+\frac{9529021297663808398605}{1073741824}\cdot t^{67}-\frac{4733806773298975596477}{1073741824}\cdot t^{65}+\frac{4302801673794934104051}{2147483648}\cdot t^{63}-\frac{27944353264972566093}{33554432}\cdot t^{61}+\frac{10871565780133899034815}{34359738368}\cdot t^{59}-\frac{3772494758053042728369}{34359738368}\cdot t^{57}+\frac{9555522272543180554695}{274877906944}\cdot t^{55}-\frac{1378524666698183006541}{137438953472}\cdot t^{53}+\frac{92649552125749259034537}{35184372088832}\cdot t^{51}-\frac{22093166755341763458325}{35184372088832}\cdot t^{49}+\frac{76404648305293558483415}{562949953421312}\cdot t^{47}-\frac{3733307371493250734365}{140737488355328}\cdot t^{45}+\frac{42112905191506924164005}{9007199254740992}\cdot t^{43}-\frac{6672888730264781681335}{9007199254740992}\cdot t^{41}+\frac{7577464366992912322525}{72057594037927936}\cdot t^{39}-\frac{479832437466723194301}{36028797018963968}\cdot t^{37}+\frac{3454263348172045978863}{2305843009213693952}\cdot t^{35}-\frac{343296228235431431751}{2305843009213693952}\cdot t^{33}+\frac{119862818931975642523}{9223372036854775808}\cdot t^{31}-\frac{1140837969150818785}{1152921504606846976}\cdot t^{29}+\frac{9623045990488650979}{147573952589676412928}\cdot t^{27}-\frac{543827757824587509}{147573952589676412928}\cdot t^{25}+\frac{208597527059309115}{1180591620717411303424}\cdot t^{23}-\frac{4189192308265965}{590295810358705651712}\cdot t^{21}+\frac{17769600161033175}{75557863725914323419136}\cdot t^{19}-\frac{476944215582195}{75557863725914323419136}\cdot t^{17}+\frac{648544433816871}{4835703278458516698824704}\cdot t^{15}-\frac{2648875549191}{1208925819614629174706176}\cdot t^{13}+\frac{2050427055873}{77371252455336267181195264}\cdot t^{11}-\frac{17438315235}{77371252455336267181195264}\cdot t^9+\frac{774917033}{618970019642690137449562112}\cdot t^7-\frac{1253525}{309485009821345068724781056}\cdot t^5+\frac{123481}{19807040628566084398385987584}\cdot t^3-\frac{57}{19807040628566084398385987584}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Chebyshev T (first kind) type can be downloaded here packed into a single file.