Rule: Q[1, 6, 28, 36]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^7-\frac{7}{4}\cdot t^5+\frac{7}{8}\cdot t^3-\frac{7}{64}\cdot t$
• $P_3$:
  $t^{35}-\frac{35}{4}\cdot t^{33}+35\cdot t^{31}-\frac{5425}{64}\cdot t^{29}+\frac{35525}{256}\cdot t^{27}-\frac{166257}{1024}\cdot t^{25}+\frac{143325}{1024}\cdot t^{23}-\frac{740025}{8192}\cdot t^{21}+\frac{2877875}{65536}\cdot t^{19}-\frac{4206125}{262144}\cdot t^{17}+\frac{572033}{131072}\cdot t^{15}-\frac{1820105}{2097152}\cdot t^{13}+\frac{1028755}{8388608}\cdot t^{11}-\frac{395675}{33554432}\cdot t^9+\frac{24225}{33554432}\cdot t^7-\frac{6783}{268435456}\cdot t^5+\frac{1785}{4294967296}\cdot t^3-\frac{35}{17179869184}\cdot t$
• $P_4$:
  $t^{71}-18\cdot t^{69}+\frac{2483}{16}\cdot t^{67}-\frac{13651}{16}\cdot t^{65}+\frac{53755}{16}\cdot t^{63}-\frac{20181}{2}\cdot t^{61}+\frac{98443569}{4096}\cdot t^{59}-\frac{190894559}{4096}\cdot t^{57}+\frac{4912012373}{65536}\cdot t^{55}-\frac{3320306715}{32768}\cdot t^{53}+\frac{121960926945}{1048576}\cdot t^{51}-\frac{119751427965}{1048576}\cdot t^{49}+\frac{404513667285}{4194304}\cdot t^{47}-\frac{73735231605}{1048576}\cdot t^{45}+\frac{5956599951225}{134217728}\cdot t^{43}-\frac{3258565443315}{134217728}\cdot t^{41}+\frac{49461886528915}{4294967296}\cdot t^{39}-\frac{10165486498895}{2147483648}\cdot t^{37}+\frac{115683261704605}{68719476736}\cdot t^{35}-\frac{35502394120725}{68719476736}\cdot t^{33}+\frac{18737662609897}{137438953472}\cdot t^{31}-\frac{264500680961}{8589934592}\cdot t^{29}+\frac{52045427380169}{8796093022208}\cdot t^{27}-\frac{8446127688063}{8796093022208}\cdot t^{25}+\frac{18353689330275}{140737488355328}\cdot t^{23}-\frac{1031465905041}{70368744177664}\cdot t^{21}+\frac{3028248784491}{2251799813685248}\cdot t^{19}-\frac{222919877831}{2251799813685248}\cdot t^{17}+\frac{51538723353}{9007199254740992}\cdot t^{15}-\frac{568688335}{2251799813685248}\cdot t^{13}+\frac{2364780223}{288230376151711744}\cdot t^{11}-\frac{53767549}{288230376151711744}\cdot t^9+\frac{50916921}{18446744073709551616}\cdot t^7-\frac{218841}{9223372036854775808}\cdot t^5+\frac{28595}{295147905179352825856}\cdot t^3-\frac{35}{295147905179352825856}\cdot t$

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.