Rule: Q[1, 2, 12, 90]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{4}\cdot t$
• $P_3$:
  $t^{15}-\frac{15}{4}\cdot t^{13}+\frac{45}{8}\cdot t^{11}-\frac{275}{64}\cdot t^9+\frac{225}{128}\cdot t^7-\frac{189}{512}\cdot t^5+\frac{35}{1024}\cdot t^3-\frac{15}{16384}\cdot t$
• $P_4$:
  $t^{105}-\frac{105}{4}\cdot t^{103}+\frac{5355}{16}\cdot t^{101}-\frac{88375}{32}\cdot t^{99}+\frac{4244625}{256}\cdot t^{97}-\frac{9881487}{128}\cdot t^{95}+\frac{148555015}{512}\cdot t^{93}-\frac{926411595}{1024}\cdot t^{91}+\frac{39109850325}{16384}\cdot t^{89}-\frac{1418094202525}{262144}\cdot t^{87}+\frac{11168611392939}{1048576}\cdot t^{85}-\frac{38560872991095}{2097152}\cdot t^{83}+\frac{470332081679915}{16777216}\cdot t^{81}-\frac{637071883211925}{16777216}\cdot t^{79}+\frac{3081347680025025}{67108864}\cdot t^{77}-\frac{6678535786483869}{134217728}\cdot t^{75}+\frac{208235245028008275}{4294967296}\cdot t^{73}-\frac{731607251248136025}{17179869184}\cdot t^{71}+\frac{2321895299299639875}{68719476736}\cdot t^{69}-\frac{3333639150646851375}{137438953472}\cdot t^{67}+\frac{17342767440188678565}{1099511627776}\cdot t^{65}-\frac{2556190212272707725}{274877906944}\cdot t^{63}+\frac{5467951242681925725}{1099511627776}\cdot t^{61}-\frac{5305594259866343625}{2199023255552}\cdot t^{59}+\frac{37357497031404584125}{35184372088832}\cdot t^{57}-\frac{119245130524243432527}{281474976710656}\cdot t^{55}+\frac{172423582111491233985}{1125899906842624}\cdot t^{53}-\frac{112820368542086856805}{2251799813685248}\cdot t^{51}+\frac{266875639872283381125}{18014398509481984}\cdot t^{49}-\frac{71199127152859631625}{18014398509481984}\cdot t^{47}+\frac{68414450179770010477}{72057594037927936}\cdot t^{45}-\frac{29524980679150963545}{144115188075855872}\cdot t^{43}+\frac{365219966483196165495}{9223372036854775808}\cdot t^{41}-\frac{252087855653384558675}{36893488147419103232}\cdot t^{39}+\frac{154761475591680164025}{147573952589676412928}\cdot t^{37}-\frac{42069854181248567037}{295147905179352825856}\cdot t^{35}+\frac{40308475423257483715}{2361183241434822606848}\cdot t^{33}-\frac{2114753082619232055}{1180591620717411303424}\cdot t^{31}+\frac{772474613839703775}{4722366482869645213696}\cdot t^{29}-\frac{121843315158865475}{9444732965739290427392}\cdot t^{27}+\frac{131590780371574713}{151115727451828646838272}\cdot t^{25}-\frac{240714842143124475}{4835703278458516698824704}\cdot t^{23}+\frac{46032392337271725}{19342813113834066795298816}\cdot t^{21}-\frac{3625957385906625}{38685626227668133590597632}\cdot t^{19}+\frac{924051733219125}{309485009821345068724781056}\cdot t^{17}-\frac{23272414021815}{309485009821345068724781056}\cdot t^{15}+\frac{1800739478475}{1237940039285380274899124224}\cdot t^{13}-\frac{51525194175}{2475880078570760549798248448}\cdot t^{11}+\frac{16572430875}{79228162514264337593543950336}\cdot t^9-\frac{434845125}{316912650057057350374175801344}\cdot t^7+\frac{6641271}{1267650600228229401496703205376}\cdot t^5-\frac{24115}{2535301200456458802993406410752}\cdot t^3+\frac{105}{20282409603651670423947251286016}\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.