Rule: Q[3, 84]

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.

• $P_1$:
  $4\cdot t^3-3\cdot t$
• $P_2$:
  $4\cdot t^{87}-87\cdot t^{85}+\frac{1827}{2}\cdot t^{83}-\frac{98687}{16}\cdot t^{81}+\frac{481545}{16}\cdot t^{79}-\frac{7237269}{64}\cdot t^{77}+\frac{43572529}{128}\cdot t^{75}-\frac{3454679085}{4096}\cdot t^{73}+\frac{28730685555}{16384}\cdot t^{71}-\frac{203406705425}{65536}\cdot t^{69}+\frac{619730040165}{131072}\cdot t^{67}-\frac{6556091477535}{1048576}\cdot t^{65}+\frac{1893981982399}{262144}\cdot t^{63}-\frac{7690118111487}{1048576}\cdot t^{61}+\frac{13769976657555}{2097152}\cdot t^{59}-\frac{174521704156123}{33554432}\cdot t^{57}+\frac{980762816313987}{268435456}\cdot t^{55}-\frac{2447786188615581}{1073741824}\cdot t^{53}+\frac{2715820747111329}{2147483648}\cdot t^{51}-\frac{10720345054386825}{17179869184}\cdot t^{49}+\frac{4704151411924965}{17179869184}\cdot t^{47}-\frac{7337933154820905}{68719476736}\cdot t^{45}+\frac{5080107568722165}{137438953472}\cdot t^{43}-\frac{199449440632874565}{17592186044416}\cdot t^{41}+\frac{216334049363699925}{70368744177664}\cdot t^{39}-\frac{206843265262582767}{281474976710656}\cdot t^{37}+\frac{86858521226280027}{562949953421312}\cdot t^{35}-\frac{127606963283053373}{4503599627370496}\cdot t^{33}+\frac{10196198034723393}{2251799813685248}\cdot t^{31}-\frac{5637612468663945}{9007199254740992}\cdot t^{29}+\frac{1338520855133077}{18014398509481984}\cdot t^{27}-\frac{2165072903924931}{288230376151711744}\cdot t^{25}+\frac{2952372141715815}{4611686018427387904}\cdot t^{23}-\frac{838327892092145}{18446744073709551616}\cdot t^{21}+\frac{97696369222725}{36893488147419103232}\cdot t^{19}-\frac{36716657444145}{295147905179352825856}\cdot t^{17}+\frac{1359876201635}{295147905179352825856}\cdot t^{15}-\frac{154364325591}{1180591620717411303424}\cdot t^{13}+\frac{6466389579}{2361183241434822606848}\cdot t^{11}-\frac{3039755785}{75557863725914323419136}\cdot t^9+\frac{116416179}{302231454903657293676544}\cdot t^7-\frac{2592513}{1208925819614629174706176}\cdot t^5+\frac{13717}{2417851639229258349412352}\cdot t^3-\frac{87}{19342813113834066795298816}\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.