Rule: Q[6, 72]

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.

• $P_1$:
  $32\cdot t^6-48\cdot t^4+18\cdot t^2-1$
• $P_2$:
  $32\cdot t^{78}-624\cdot t^{76}+5850\cdot t^{74}-35113\cdot t^{72}+\frac{606411}{4}\cdot t^{70}-\frac{4012281}{8}\cdot t^{68}+\frac{169258817}{128}\cdot t^{66}-\frac{730503345}{256}\cdot t^{64}+\frac{1314906021}{256}\cdot t^{62}-\frac{4004005291}{512}\cdot t^{60}+\frac{41688760971}{4096}\cdot t^{58}-\frac{93502743399}{8192}\cdot t^{56}+\frac{363621779885}{32768}\cdot t^{54}-\frac{615790256823}{65536}\cdot t^{52}+\frac{58324134324807}{8388608}\cdot t^{50}-\frac{75605359309935}{16777216}\cdot t^{48}+\frac{343882440732285}{134217728}\cdot t^{46}-\frac{343219215195675}{268435456}\cdot t^{44}+\frac{1202538435463365}{2147483648}\cdot t^{42}-\frac{923626755516465}{4294967296}\cdot t^{40}+\frac{1242118740177315}{17179869184}\cdot t^{38}-\frac{729498307723185}{34359738368}\cdot t^{36}+\frac{2984311258867575}{549755813888}\cdot t^{34}-\frac{1323477166976055}{1099511627776}\cdot t^{32}+\frac{506515952793305}{2199023255552}\cdot t^{30}-\frac{166290142992519}{4398046511104}\cdot t^{28}+\frac{185969449855539}{35184372088832}\cdot t^{26}-\frac{43892571679775}{70368744177664}\cdot t^{24}+\frac{17306213976597}{281474976710656}\cdot t^{22}-\frac{2813325424767}{562949953421312}\cdot t^{20}+\frac{5939242563397}{18014398509481984}\cdot t^{18}-\frac{623681614413}{36028797018963968}\cdot t^{16}+\frac{406748878965}{576460752303423488}\cdot t^{14}-\frac{24925352179}{1152921504606846976}\cdot t^{12}+\frac{4398591561}{9223372036854775808}\cdot t^{10}-\frac{131519349}{18446744073709551616}\cdot t^8+\frac{4871087}{73786976294838206464}\cdot t^6-\frac{48165}{147573952589676412928}\cdot t^4+\frac{1521}{2361183241434822606848}\cdot t^2-\frac{1}{4722366482869645213696}$

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.