Rule: Q[8, 80]

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.

• $P_1$:
  $128\cdot t^8-256\cdot t^6+160\cdot t^4-32\cdot t^2+1$
• $P_2$:
  $128\cdot t^{88}-2816\cdot t^{86}+29920\cdot t^{84}-204512\cdot t^{82}+1010691\cdot t^{80}-3847932\cdot t^{78}+\frac{23486463}{2}\cdot t^{76}-\frac{59026825}{2}\cdot t^{74}+\frac{31886290865}{512}\cdot t^{72}-\frac{28657299385}{256}\cdot t^{70}+\frac{354909630845}{2048}\cdot t^{68}-\frac{477263364265}{2048}\cdot t^{66}+\frac{17960173971025}{65536}\cdot t^{64}-\frac{1160503548897}{4096}\cdot t^{62}+\frac{8473020119553}{32768}\cdot t^{60}-\frac{6848057356899}{32768}\cdot t^{58}+\frac{1257759867883783}{8388608}\cdot t^{56}-\frac{401191010054065}{4194304}\cdot t^{54}+\frac{1822553445674181}{33554432}\cdot t^{52}-\frac{921703229963373}{33554432}\cdot t^{50}+\frac{13283370078883905}{1073741824}\cdot t^{48}-\frac{1331169282958515}{268435456}\cdot t^{46}+\frac{3795482666286675}{2147483648}\cdot t^{44}-\frac{1200845017494045}{2147483648}\cdot t^{42}+\frac{344642520020790915}{2199023255552}\cdot t^{40}-\frac{42670026288288399}{1099511627776}\cdot t^{38}+\frac{74434313847808299}{8796093022208}\cdot t^{36}-\frac{14236070954498855}{8796093022208}\cdot t^{34}+\frac{76061293385465311}{281474976710656}\cdot t^{32}-\frac{1378083047895631}{35184372088832}\cdot t^{30}+\frac{1378083047895631}{281474976710656}\cdot t^{28}-\frac{147401073034677}{281474976710656}\cdot t^{26}+\frac{6843621248038575}{144115188075855872}\cdot t^{24}-\frac{260170725132045}{72057594037927936}\cdot t^{22}+\frac{130935593693905}{576460752303423488}\cdot t^{20}-\frac{6705596442545}{576460752303423488}\cdot t^{18}+\frac{8768856886405}{18446744073709551616}\cdot t^{16}-\frac{69704744725}{4611686018427387904}\cdot t^{14}+\frac{13353961621}{36893488147419103232}\cdot t^{12}-\frac{230602163}{36893488147419103232}\cdot t^{10}+\frac{691806489}{9444732965739290427392}\cdot t^8-\frac{2513049}{4722366482869645213696}\cdot t^6+\frac{78045}{37778931862957161709568}\cdot t^4-\frac{121}{37778931862957161709568}\cdot t^2+\frac{1}{1208925819614629174706176}$

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.