Rule: Q[1, 4, 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.

• $P_1$:
  $t$
• $P_2$:
  $t^5-\frac{5}{4}\cdot t^3+\frac{5}{16}\cdot t$
• $P_3$:
  $t^{95}-\frac{95}{4}\cdot t^{93}+\frac{2185}{8}\cdot t^{91}-\frac{129675}{64}\cdot t^{89}+\frac{1395075}{128}\cdot t^{87}-\frac{23195447}{512}\cdot t^{85}+\frac{155070685}{1024}\cdot t^{83}-\frac{6853318715}{16384}\cdot t^{81}+\frac{31903380225}{32768}\cdot t^{79}-\frac{253990476675}{131072}\cdot t^{77}+\frac{874324864413}{262144}\cdot t^{75}-\frac{10503253241325}{2097152}\cdot t^{73}+\frac{27713403130725}{4194304}\cdot t^{71}-\frac{129207892645125}{16777216}\cdot t^{69}+\frac{267303100657375}{33554432}\cdot t^{67}-\frac{7880095407379415}{1073741824}\cdot t^{65}+\frac{6483622803540025}{1073741824}\cdot t^{63}-\frac{19098816493685775}{4294967296}\cdot t^{61}+\frac{25217052080407625}{8589934592}\cdot t^{59}-\frac{119519047394951375}{68719476736}\cdot t^{57}+\frac{127168266428228263}{137438953472}\cdot t^{55}-\frac{243043597999895715}{549755813888}\cdot t^{53}+\frac{208539276490570545}{1099511627776}\cdot t^{51}-\frac{1284481050847717125}{17592186044416}\cdot t^{49}+\frac{886472837908987875}{35184372088832}\cdot t^{47}-\frac{1095173871748132449}{140737488355328}\cdot t^{45}+\frac{604360163339270415}{281474976710656}\cdot t^{43}-\frac{1188969994543270555}{2251799813685248}\cdot t^{41}+\frac{519699038126589475}{4503599627370496}\cdot t^{39}-\frac{402400195665415675}{18014398509481984}\cdot t^{37}+\frac{137435143750341969}{36028797018963968}\cdot t^{35}-\frac{2637868081659789405}{4611686018427387904}\cdot t^{33}+\frac{1381740423726556355}{18446744073709551616}\cdot t^{31}-\frac{628063828966616525}{73786976294838206464}\cdot t^{29}+\frac{122947885516126475}{147573952589676412928}\cdot t^{27}-\frac{82199443459353129}{1180591620717411303424}\cdot t^{25}+\frac{11610090884089425}{2361183241434822606848}\cdot t^{23}-\frac{2737514439584925}{9444732965739290427392}\cdot t^{21}+\frac{265409987217375}{18889465931478580854784}\cdot t^{19}-\frac{166245816169125}{302231454903657293676544}\cdot t^{17}+\frac{10277014090455}{604462909807314587353088}\cdot t^{15}-\frac{974784534325}{2417851639229258349412352}\cdot t^{13}+\frac{34156870475}{4835703278458516698824704}\cdot t^{11}-\frac{3360693875}{38685626227668133590597632}\cdot t^9+\frac{53914875}{77371252455336267181195264}\cdot t^7-\frac{1006411}{309485009821345068724781056}\cdot t^5+\frac{4465}{618970019642690137449562112}\cdot t^3-\frac{95}{19807040628566084398385987584}\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.