Rule: Q[1, 44, 46]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{45}-22\cdot t^{43}+\frac{903}{8}\cdot t^{41}-\frac{1435}{4}\cdot t^{39}+\frac{50635}{64}\cdot t^{37}-\frac{82251}{64}\cdot t^{35}+\frac{3262623}{2048}\cdot t^{33}-\frac{394383}{256}\cdot t^{31}+\frac{9652005}{8192}\cdot t^{29}-\frac{5883955}{8192}\cdot t^{27}+\frac{45894849}{131072}\cdot t^{25}-\frac{8940555}{65536}\cdot t^{23}+\frac{44352165}{1048576}\cdot t^{21}-\frac{10855425}{1048576}\cdot t^{19}+\frac{265182525}{134217728}\cdot t^{17}-\frac{9694845}{33554432}\cdot t^{15}+\frac{67863915}{2147483648}\cdot t^{13}-\frac{5368545}{2147483648}\cdot t^{11}+\frac{4686825}{34359738368}\cdot t^9-\frac{82225}{17179869184}\cdot t^7+\frac{26565}{274877906944}\cdot t^5-\frac{253}{274877906944}\cdot t^3+\frac{23}{8796093022208}\cdot t$
• $P_3$:
  $2\cdot t^{91}-45\cdot t^{89}+\frac{979}{2}\cdot t^{87}-\frac{13717}{4}\cdot t^{85}+\frac{2225895}{128}\cdot t^{83}-\frac{17413151}{256}\cdot t^{81}+\frac{54669195}{256}\cdot t^{79}-\frac{283085361}{512}\cdot t^{77}+\frac{19721613483}{16384}\cdot t^{75}-\frac{73263021975}{32768}\cdot t^{73}+\frac{234799050915}{65536}\cdot t^{71}-\frac{654854816525}{131072}\cdot t^{69}+\frac{51209646652255}{8388608}\cdot t^{67}-\frac{110247837145215}{16777216}\cdot t^{65}+\frac{26249485034575}{4194304}\cdot t^{63}-\frac{44385492876645}{8388608}\cdot t^{61}+\frac{2137511893796325}{536870912}\cdot t^{59}-\frac{2868457137478833}{1073741824}\cdot t^{57}+\frac{3436980173735899}{2147483648}\cdot t^{55}-\frac{3679823762074845}{4294967296}\cdot t^{53}+\frac{56342190490434849}{137438953472}\cdot t^{51}-\frac{48179941566267225}{274877906944}\cdot t^{49}+\frac{18395977688938395}{274877906944}\cdot t^{47}-\frac{12530593498262385}{549755813888}\cdot t^{45}+\frac{121620466306664325}{17592186044416}\cdot t^{43}-\frac{65566137955174857}{35184372088832}\cdot t^{41}+\frac{31331138183708265}{70368744177664}\cdot t^{39}-\frac{13228702788676823}{140737488355328}\cdot t^{37}+\frac{629308289804197437}{36028797018963968}\cdot t^{35}-\frac{204947144189106445}{72057594037927936}\cdot t^{33}+\frac{14544636039226909}{36028797018963968}\cdot t^{31}-\frac{3576549845711535}{72057594037927936}\cdot t^{29}+\frac{48402641245296107}{9223372036854775808}\cdot t^{27}-\frac{8725899885515631}{18446744073709551616}\cdot t^{25}+\frac{1327469556620025}{36893488147419103232}\cdot t^{23}-\frac{168345763320735}{73786976294838206464}\cdot t^{21}+\frac{280576272201225}{2361183241434822606848}\cdot t^{19}-\frac{23576679383985}{4722366482869645213696}\cdot t^{17}+\frac{781293468865}{4722366482869645213696}\cdot t^{15}-\frac{39688347475}{9444732965739290427392}\cdot t^{13}+\frac{23813008485}{302231454903657293676544}\cdot t^{11}-\frac{626358425}{604462909807314587353088}\cdot t^9+\frac{10737573}{1208925819614629174706176}\cdot t^7-\frac{107019}{2417851639229258349412352}\cdot t^5+\frac{16215}{154742504910672534362390528}\cdot t^3-\frac{23}{309485009821345068724781056}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Chebyshev U (second kind) type can be downloaded here packed into a single file.