Rule: Q[1, 12, 78]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{13}-\frac{13}{4}\cdot t^{11}+\frac{65}{16}\cdot t^9-\frac{39}{16}\cdot t^7+\frac{91}{128}\cdot t^5-\frac{91}{1024}\cdot t^3+\frac{13}{4096}\cdot t$
• $P_3$:
  $t^{91}-\frac{91}{4}\cdot t^{89}+\frac{1001}{4}\cdot t^{87}-\frac{113477}{64}\cdot t^{85}+\frac{2328235}{256}\cdot t^{83}-\frac{36851087}{1024}\cdot t^{81}+\frac{58528197}{512}\cdot t^{79}-\frac{1226703231}{4096}\cdot t^{77}+\frac{21622491891}{32768}\cdot t^{75}-\frac{162608170725}{131072}\cdot t^{73}+\frac{263786588065}{131072}\cdot t^{71}-\frac{11918357660755}{4194304}\cdot t^{69}+\frac{58988327156395}{16777216}\cdot t^{67}-\frac{257244953338835}{67108864}\cdot t^{65}+\frac{31022118677225}{8388608}\cdot t^{63}-\frac{212583150093405}{67108864}\cdot t^{61}+\frac{2593514431139541}{1073741824}\cdot t^{59}-\frac{7054854040826319}{4294967296}\cdot t^{57}+\frac{4284454737122833}{4294967296}\cdot t^{55}-\frac{37207106927645655}{68719476736}\cdot t^{53}+\frac{72213230065205229}{274877906944}\cdot t^{51}-\frac{125267848072294785}{1099511627776}\cdot t^{49}+\frac{24261361879614405}{549755813888}\cdot t^{47}-\frac{67075529902463355}{4398046511104}\cdot t^{45}+\frac{165186006476215725}{35184372088832}\cdot t^{43}-\frac{180803592543057939}{140737488355328}\cdot t^{41}+\frac{43863593457191571}{140737488355328}\cdot t^{39}-\frac{1203811953769590893}{18014398509481984}\cdot t^{37}+\frac{909000863050507409}{72057594037927936}\cdot t^{35}-\frac{601619036168022145}{288230376151711744}\cdot t^{33}+\frac{21697735730649979}{72057594037927936}\cdot t^{31}-\frac{21697735730649979}{576460752303423488}\cdot t^{29}+\frac{74654921242744843}{18446744073709551616}\cdot t^{27}-\frac{27381272054549049}{73786976294838206464}\cdot t^{25}+\frac{2119293502674075}{73786976294838206464}\cdot t^{23}-\frac{2188494923169555}{1180591620717411303424}\cdot t^{21}+\frac{464226195823845}{4722366482869645213696}\cdot t^{19}-\frac{79462141627505}{18889465931478580854784}\cdot t^{17}+\frac{1341466144655}{9444732965739290427392}\cdot t^{15}-\frac{277818432325}{75557863725914323419136}\cdot t^{13}+\frac{42489877885}{604462909807314587353088}\cdot t^{11}-\frac{2279944667}{2417851639229258349412352}\cdot t^9+\frac{19941207}{2417851639229258349412352}\cdot t^7-\frac{3246243}{77371252455336267181195264}\cdot t^5+\frac{31395}{309485009821345068724781056}\cdot t^3-\frac{91}{1237940039285380274899124224}\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.