Rule: Q[8, 96]

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^{104}-3328\cdot t^{102}+42016\cdot t^{100}-343200\cdot t^{98}+2039037\cdot t^{96}-9391928\cdot t^{94}+34908263\cdot t^{92}-107603821\cdot t^{90}+\frac{143651101035}{512}\cdot t^{88}-\frac{160788425369}{256}\cdot t^{86}+\frac{2500773169037}{2048}\cdot t^{84}-\frac{4260848126717}{2048}\cdot t^{82}+\frac{205076472881553}{65536}\cdot t^{80}-\frac{68474392889445}{16384}\cdot t^{78}+\frac{652789212212709}{131072}\cdot t^{76}-\frac{696797473710195}{131072}\cdot t^{74}+\frac{171095452408294245}{33554432}\cdot t^{72}-\frac{73921564630764045}{16777216}\cdot t^{70}+\frac{461293484711357025}{134217728}\cdot t^{68}-\frac{325333299743799165}{134217728}\cdot t^{66}+\frac{6646094551909040085}{4294967296}\cdot t^{64}-\frac{240220285008760485}{268435456}\cdot t^{62}+\frac{1007220751555578885}{2147483648}\cdot t^{60}-\frac{478470405328334575}{2147483648}\cdot t^{58}+\frac{52727438667182470165}{549755813888}\cdot t^{56}-\frac{10278513360438101779}{274877906944}\cdot t^{54}+\frac{29010951910822334607}{2199023255552}\cdot t^{52}-\frac{9251688848905823879}{2199023255552}\cdot t^{50}+\frac{85212923608343114675}{70368744177664}\cdot t^{48}-\frac{5524148151161553641}{17592186044416}\cdot t^{46}+\frac{10301789795409383817}{140737488355328}\cdot t^{44}-\frac{2153224292191179207}{140737488355328}\cdot t^{42}+\frac{205991790619622810803}{72057594037927936}\cdot t^{40}-\frac{17144003060531988095}{36028797018963968}\cdot t^{38}+\frac{20255855716897458203}{288230376151711744}\cdot t^{36}-\frac{2642068136986624983}{288230376151711744}\cdot t^{34}+\frac{9687583168950958271}{9223372036854775808}\cdot t^{32}-\frac{121143637852956719}{1152921504606846976}\cdot t^{30}+\frac{84047021476931695}{9223372036854775808}\cdot t^{28}-\frac{6266227636741653}{9223372036854775808}\cdot t^{26}+\frac{407304796388207445}{9444732965739290427392}\cdot t^{24}-\frac{10880383643355135}{4722366482869645213696}\cdot t^{22}+\frac{3860781292803435}{37778931862957161709568}\cdot t^{20}-\frac{139830050635275}{37778931862957161709568}\cdot t^{18}+\frac{129660592407255}{1208925819614629174706176}\cdot t^{16}-\frac{732545719815}{302231454903657293676544}\cdot t^{14}+\frac{99942519495}{2417851639229258349412352}\cdot t^{12}-\frac{1231094865}{2417851639229258349412352}\cdot t^{10}+\frac{2638060425}{618970019642690137449562112}\cdot t^8-\frac{6852105}{309485009821345068724781056}\cdot t^6+\frac{152269}{2475880078570760549798248448}\cdot t^4-\frac{169}{2475880078570760549798248448}\cdot t^2+\frac{1}{79228162514264337593543950336}$

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.