Rule: Q[10, 100]

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.

• $P_1$:
  $512\cdot t^{10}-1280\cdot t^8+1120\cdot t^6-400\cdot t^4+50\cdot t^2-1$
• $P_2$:
  $512\cdot t^{110}-14080\cdot t^{108}+188320\cdot t^{106}-1632400\cdot t^{104}+10310300\cdot t^{102}-50579386\cdot t^{100}+\frac{1604922825}{8}\cdot t^{98}-\frac{10580025225}{16}\cdot t^{96}+\frac{59123670375}{32}\cdot t^{94}-\frac{284300949625}{64}\cdot t^{92}+\frac{4760335100521}{512}\cdot t^{90}-\frac{17507017518445}{1024}\cdot t^{88}+\frac{113974256905795}{4096}\cdot t^{86}-\frac{330353615377225}{8192}\cdot t^{84}+\frac{27419350076309675}{524288}\cdot t^{82}-\frac{63901516914683811}{1048576}\cdot t^{80}+\frac{537044663431917135}{8388608}\cdot t^{78}-\frac{1020079142495918505}{16777216}\cdot t^{76}+\frac{7022283951964656375}{134217728}\cdot t^{74}-\frac{10970034097314364875}{268435456}\cdot t^{72}+\frac{31154896836372796245}{1073741824}\cdot t^{70}-\frac{40256327372841253575}{2147483648}\cdot t^{68}+\frac{378941792377406510925}{34359738368}\cdot t^{66}-\frac{406211966341597684125}{68719476736}\cdot t^{64}+\frac{198382588213338403875}{68719476736}\cdot t^{62}-\frac{176537164381846080813}{137438953472}\cdot t^{60}+\frac{572290807611479053185}{1099511627776}\cdot t^{58}-\frac{422131506015963799605}{2199023255552}\cdot t^{56}+\frac{566273971484829487275}{8796093022208}\cdot t^{54}-\frac{344971499870068538225}{17592186044416}\cdot t^{52}+\frac{3049548058851405877909}{562949953421312}\cdot t^{50}-\frac{1525396640299294487725}{1125899906842624}\cdot t^{48}+\frac{5514895545697449301775}{18014398509481984}\cdot t^{46}-\frac{2246326993229775689625}{36028797018963968}\cdot t^{44}+\frac{3289512903398402170875}{288230376151711744}\cdot t^{42}-\frac{1078960232314675912047}{576460752303423488}\cdot t^{40}+\frac{631823559463548957505}{2305843009213693952}\cdot t^{38}-\frac{164447227805581235515}{4611686018427387904}\cdot t^{36}+\frac{302929103852386486475}{73786976294838206464}\cdot t^{34}-\frac{61373502080602679275}{147573952589676412928}\cdot t^{32}+\frac{10871877511421046043}{295147905179352825856}\cdot t^{30}-\frac{1671709691575876645}{590295810358705651712}\cdot t^{28}+\frac{885022777893111165}{4722366482869645213696}\cdot t^{26}-\frac{99837696221888625}{9444732965739290427392}\cdot t^{24}+\frac{18977413331433375}{37778931862957161709568}\cdot t^{22}-\frac{1498729052841405}{75557863725914323419136}\cdot t^{20}+\frac{6190402609562325}{9671406556917033397649408}\cdot t^{18}-\frac{319868827849725}{19342813113834066795298816}\cdot t^{16}+\frac{51591746427375}{154742504910672534362390528}\cdot t^{14}-\frac{1570708907625}{309485009821345068724781056}\cdot t^{12}+\frac{138222383871}{2475880078570760549798248448}\cdot t^{10}-\frac{2067134355}{4951760157141521099596496896}\cdot t^8+\frac{38381805}{19807040628566084398385987584}\cdot t^6-\frac{190575}{39614081257132168796771975168}\cdot t^4+\frac{3025}{633825300114114700748351602688}\cdot t^2-\frac{1}{1267650600228229401496703205376}$

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.