Rule: Q[1, 40, 42]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{41}-\frac{41}{4}\cdot t^{39}+\frac{779}{16}\cdot t^{37}-\frac{4551}{32}\cdot t^{35}+\frac{73185}{256}\cdot t^{33}-\frac{53669}{128}\cdot t^{31}+\frac{237677}{512}\cdot t^{29}-\frac{405449}{1024}\cdot t^{27}+\frac{4312503}{16384}\cdot t^{25}-\frac{35937525}{262144}\cdot t^{23}+\frac{58659315}{1048576}\cdot t^{21}-\frac{37328655}{2097152}\cdot t^{19}+\frac{73370115}{16777216}\cdot t^{17}-\frac{13706505}{16777216}\cdot t^{15}+\frac{7614725}{67108864}\cdot t^{13}-\frac{1522945}{134217728}\cdot t^{11}+\frac{3350479}{4294967296}\cdot t^9-\frac{591261}{17179869184}\cdot t^7+\frac{59983}{68719476736}\cdot t^5-\frac{1435}{137438953472}\cdot t^3+\frac{41}{1099511627776}\cdot t$
• $P_3$:
  $t^{83}-21\cdot t^{81}+\frac{3401}{16}\cdot t^{79}-\frac{5525}{4}\cdot t^{77}+\frac{1657579}{256}\cdot t^{75}-\frac{5971985}{256}\cdot t^{73}+\frac{137629455}{2048}\cdot t^{71}-\frac{162813579}{1024}\cdot t^{69}+\frac{20640442305}{65536}\cdot t^{67}-\frac{34720377329}{65536}\cdot t^{65}+\frac{100273759157}{131072}\cdot t^{63}-\frac{3916792061}{4096}\cdot t^{61}+\frac{2183806885741}{2097152}\cdot t^{59}-\frac{2082158136035}{2097152}\cdot t^{57}+\frac{13958588707697}{16777216}\cdot t^{55}-\frac{5154822841707}{8388608}\cdot t^{53}+\frac{430378742828151}{1073741824}\cdot t^{51}-\frac{248222120190795}{1073741824}\cdot t^{49}+\frac{8106194519678325}{68719476736}\cdot t^{47}-\frac{914808642643455}{17179869184}\cdot t^{45}+\frac{23364978736232595}{1099511627776}\cdot t^{43}-\frac{8232763135095345}{1099511627776}\cdot t^{41}+\frac{20451120164687415}{8796093022208}\cdot t^{39}-\frac{2791046030456775}{4398046511104}\cdot t^{37}+\frac{42719234588752995}{281474976710656}\cdot t^{35}-\frac{8915937632568603}{281474976710656}\cdot t^{33}+\frac{6464589917377977}{1125899906842624}\cdot t^{31}-\frac{126479131407559}{140737488355328}\cdot t^{29}+\frac{2172923466125125}{18014398509481984}\cdot t^{27}-\frac{248038436099363}{18014398509481984}\cdot t^{25}+\frac{190742247267145}{144115188075855872}\cdot t^{23}-\frac{7628634009535}{72057594037927936}\cdot t^{21}+\frac{128123043930959}{18446744073709551616}\cdot t^{19}-\frac{6772585417995}{18446744073709551616}\cdot t^{17}+\frac{4513717165821}{295147905179352825856}\cdot t^{15}-\frac{36003011061}{73786976294838206464}\cdot t^{13}+\frac{54249295919}{4722366482869645213696}\cdot t^{11}-\frac{895743277}{4722366482869645213696}\cdot t^9+\frac{77122435}{37778931862957161709568}\cdot t^7-\frac{241367}{18889465931478580854784}\cdot t^5+\frac{45961}{1208925819614629174706176}\cdot t^3-\frac{41}{1208925819614629174706176}\cdot t$

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.