Rule: Q[8, 32, 41]

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.

• $P_1$:
  $128\cdot t^8-256\cdot t^6+160\cdot t^4-32\cdot t^2+1$
• $P_2$:
  $128\cdot t^{40}-1280\cdot t^{38}+5920\cdot t^{36}-16800\cdot t^{34}+32725\cdot t^{32}-46376\cdot t^{30}+49445\cdot t^{28}-40455\cdot t^{26}+\frac{13147875}{512}\cdot t^{24}-\frac{3251625}{256}\cdot t^{22}+\frac{10015005}{2048}\cdot t^{20}-\frac{2982525}{2048}\cdot t^{18}+\frac{21729825}{65536}\cdot t^{16}-\frac{928625}{16384}\cdot t^{14}+\frac{928625}{131072}\cdot t^{12}-\frac{81719}{131072}\cdot t^{10}+\frac{1225785}{33554432}\cdot t^8-\frac{21945}{16777216}\cdot t^6+\frac{3325}{134217728}\cdot t^4-\frac{25}{134217728}\cdot t^2+\frac{1}{4294967296}$
• $P_3$:
  $128\cdot t^{81}-2624\cdot t^{79}+25904\cdot t^{77}-164008\cdot t^{75}+748325\cdot t^{73}-\frac{5242641}{2}\cdot t^{71}+\frac{58666377}{8}\cdot t^{69}-\frac{269253939}{16}\cdot t^{67}+\frac{2066445557}{64}\cdot t^{65}-\frac{6724376945}{128}\cdot t^{63}+\frac{37510410223}{512}\cdot t^{61}-\frac{90412119473}{1024}\cdot t^{59}+\frac{758074648799}{8192}\cdot t^{57}-\frac{1388647909691}{16384}\cdot t^{55}+\frac{4462127961615}{65536}\cdot t^{53}-\frac{6304519296045}{131072}\cdot t^{51}+\frac{1004471202260565}{33554432}\cdot t^{49}-\frac{1102606665411405}{67108864}\cdot t^{47}+\frac{2135390661379815}{268435456}\cdot t^{45}-\frac{1823451793911825}{536870912}\cdot t^{43}+\frac{5486885897842965}{4294967296}\cdot t^{41}-\frac{3630225306480465}{8589934592}\cdot t^{39}+\frac{4214986347647985}{34359738368}\cdot t^{37}-\frac{2140586247441915}{68719476736}\cdot t^{35}+\frac{3789443170401525}{549755813888}\cdot t^{33}-\frac{1454693706607869}{1099511627776}\cdot t^{31}+\frac{963279451051883}{4398046511104}\cdot t^{29}-\frac{273214376948261}{8796093022208}\cdot t^{27}+\frac{263374723516751}{70368744177664}\cdot t^{25}-\frac{53406232536475}{140737488355328}\cdot t^{23}+\frac{18010091821799}{562949953421312}\cdot t^{21}-\frac{2489098783589}{1125899906842624}\cdot t^{19}+\frac{17729302242597}{144115188075855872}\cdot t^{17}-\frac{1554115724493}{288230376151711744}\cdot t^{15}+\frac{208607759535}{1152921504606846976}\cdot t^{13}-\frac{10327828537}{2305843009213693952}\cdot t^{11}+\frac{1433973073}{18446744073709551616}\cdot t^9-\frac{32436781}{36893488147419103232}\cdot t^7+\frac{853333}{147573952589676412928}\cdot t^5-\frac{5335}{295147905179352825856}\cdot t^3+\frac{5}{295147905179352825856}\cdot t$

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.