Rule: Q[2, 8, 60]

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.

• $P_1$:
  $2\cdot t^2-1$
• $P_2$:
  $2\cdot t^{10}-5\cdot t^8+\frac{35}{8}\cdot t^6-\frac{25}{16}\cdot t^4+\frac{25}{128}\cdot t^2-\frac{1}{256}$
• $P_3$:
  $2\cdot t^{70}-35\cdot t^{68}+\frac{2345}{8}\cdot t^{66}-\frac{25025}{16}\cdot t^{64}+\frac{47775}{8}\cdot t^{62}-\frac{277977}{16}\cdot t^{60}+\frac{82003215}{2048}\cdot t^{58}-\frac{307372595}{4096}\cdot t^{56}+\frac{3817369325}{32768}\cdot t^{54}-\frac{9950192175}{65536}\cdot t^{52}+\frac{87959698827}{524288}\cdot t^{50}-\frac{166025625675}{1048576}\cdot t^{48}+\frac{269076014025}{2097152}\cdot t^{46}-\frac{375834918375}{4194304}\cdot t^{44}+\frac{3627957477375}{67108864}\cdot t^{42}-\frac{3786268349115}{134217728}\cdot t^{40}+\frac{27345271410275}{2147483648}\cdot t^{38}-\frac{21335988680825}{4294967296}\cdot t^{36}+\frac{57443046448375}{34359738368}\cdot t^{34}-\frac{33256500575375}{68719476736}\cdot t^{32}+\frac{8247612142693}{68719476736}\cdot t^{30}-\frac{3486599885395}{137438953472}\cdot t^{28}+\frac{19968708434535}{4398046511104}\cdot t^{26}-\frac{6003543238875}{8796093022208}\cdot t^{24}+\frac{6003543238875}{70368744177664}\cdot t^{22}-\frac{1232727545049}{140737488355328}\cdot t^{20}+\frac{818944872585}{1125899906842624}\cdot t^{18}-\frac{107922967705}{2251799813685248}\cdot t^{16}+\frac{11012547725}{4503599627370496}\cdot t^{14}-\frac{842844275}{9007199254740992}\cdot t^{12}+\frac{370851481}{144115188075855872}\cdot t^{10}-\frac{13803405}{288230376151711744}\cdot t^8+\frac{5085465}{9223372036854775808}\cdot t^6-\frac{62475}{18446744073709551616}\cdot t^4+\frac{1225}{147573952589676412928}\cdot t^2-\frac{1}{295147905179352825856}$

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.