Rule: Q[1, 4, 20, 50]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^5-\frac{5}{4}\cdot t^3+\frac{5}{16}\cdot t$
• $P_3$:
  $t^{25}-\frac{25}{4}\cdot t^{23}+\frac{275}{16}\cdot t^{21}-\frac{875}{32}\cdot t^{19}+\frac{7125}{256}\cdot t^{17}-\frac{4845}{256}\cdot t^{15}+\frac{8925}{1024}\cdot t^{13}-\frac{5525}{2048}\cdot t^{11}+\frac{17875}{32768}\cdot t^9-\frac{17875}{262144}\cdot t^7+\frac{5005}{1048576}\cdot t^5-\frac{325}{2097152}\cdot t^3+\frac{25}{16777216}\cdot t$
• $P_4$:
  $t^{75}-\frac{75}{4}\cdot t^{73}+\frac{675}{4}\cdot t^{71}-\frac{62125}{64}\cdot t^{69}+\frac{1026375}{256}\cdot t^{67}-\frac{12967515}{1024}\cdot t^{65}+\frac{4071925}{128}\cdot t^{63}-\frac{66827475}{1024}\cdot t^{61}+\frac{912643875}{8192}\cdot t^{59}-\frac{5257689125}{32768}\cdot t^{57}+\frac{6454824495}{32768}\cdot t^{55}-\frac{871401306825}{4194304}\cdot t^{53}+\frac{3176695769325}{16777216}\cdot t^{51}-\frac{10050340213125}{67108864}\cdot t^{49}+\frac{3459953188125}{33554432}\cdot t^{47}-\frac{16623152872725}{268435456}\cdot t^{45}+\frac{139465435118625}{4294967296}\cdot t^{43}-\frac{255450888259875}{17179869184}\cdot t^{41}+\frac{102080764314375}{17179869184}\cdot t^{39}-\frac{568735686894375}{274877906944}\cdot t^{37}+\frac{688687213584825}{1099511627776}\cdot t^{35}-\frac{722696458700125}{4398046511104}\cdot t^{33}+\frac{40907346718875}{1099511627776}\cdot t^{31}-\frac{63618448910625}{8796093022208}\cdot t^{29}+\frac{84408791691875}{70368744177664}\cdot t^{27}-\frac{47403977414157}{281474976710656}\cdot t^{25}+\frac{5581316022075}{281474976710656}\cdot t^{23}-\frac{17432999426975}{9007199254740992}\cdot t^{21}+\frac{5563723221375}{36028797018963968}\cdot t^{19}-\frac{1426381815375}{144115188075855872}\cdot t^{17}+\frac{35923690165}{72057594037927936}\cdot t^{15}-\frac{11061546825}{576460752303423488}\cdot t^{13}+\frac{10032565725}{18446744073709551616}\cdot t^{11}-\frac{796235375}{73786976294838206464}\cdot t^9+\frac{10281375}{73786976294838206464}\cdot t^7-\frac{1233765}{1180591620717411303424}\cdot t^5+\frac{17575}{4722366482869645213696}\cdot t^3-\frac{75}{18889465931478580854784}\cdot t$

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.