Rule: Q[16, 34, 51]

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.

• $P_1$:
  $65536\cdot t^{16}-245760\cdot t^{14}+372736\cdot t^{12}-292864\cdot t^{10}+126720\cdot t^8-29568\cdot t^6+3360\cdot t^4-144\cdot t^2+1$
• $P_2$:
  $65536\cdot t^{50}-802816\cdot t^{48}+4620288\cdot t^{46}-16604160\cdot t^{44}+41775360\cdot t^{42}-78192576\cdot t^{40}+112944832\cdot t^{38}-128896456\cdot t^{36}+118030185\cdot t^{34}-\frac{350343565}{4}\cdot t^{32}+52978783\cdot t^{30}-\frac{419014011}{16}\cdot t^{28}+\frac{676868787}{64}\cdot t^{26}-\frac{890616825}{256}\cdot t^{24}+\frac{237268575}{256}\cdot t^{22}-\frac{405992895}{2048}\cdot t^{20}+\frac{1101980715}{32768}\cdot t^{18}-\frac{583401555}{131072}\cdot t^{16}+\frac{29464725}{65536}\cdot t^{14}-\frac{141120525}{4194304}\cdot t^{12}+\frac{30045015}{16777216}\cdot t^{10}-\frac{4292145}{67108864}\cdot t^8+\frac{94185}{67108864}\cdot t^6-\frac{8775}{536870912}\cdot t^4+\frac{325}{4294967296}\cdot t^2-\frac{1}{17179869184}$
• $P_3$:
  $65536\cdot t^{101}-1638400\cdot t^{99}+19869696\cdot t^{97}-155746304\cdot t^{95}+886999040\cdot t^{93}-3911940096\cdot t^{91}+13905724560\cdot t^{89}-40943471712\cdot t^{87}+101841441273\cdot t^{85}-217188736765\cdot t^{83}+\frac{6426898010533}{16}\cdot t^{81}-\frac{2600293400865}{4}\cdot t^{79}+\frac{59344473837519}{64}\cdot t^{77}-\frac{75039727938021}{64}\cdot t^{75}+\frac{2704353831532575}{2048}\cdot t^{73}-\frac{1361502273806055}{1024}\cdot t^{71}+\frac{78682166288559225}{65536}\cdot t^{69}-\frac{63871405575418665}{65536}\cdot t^{67}+\frac{747194062048945335}{1048576}\cdot t^{65}-\frac{30797472437020575}{65536}\cdot t^{63}+\frac{293402261802444795}{1048576}\cdot t^{61}-\frac{157826613491614925}{1048576}\cdot t^{59}+\frac{4909842466984602485}{67108864}\cdot t^{57}-\frac{1078165737108891795}{33554432}\cdot t^{55}+\frac{13684411278689780475}{1073741824}\cdot t^{53}-\frac{4897952920008965583}{1073741824}\cdot t^{51}+\frac{25282955356321583475}{17179869184}\cdot t^{49}-\frac{1835355277718159393}{4294967296}\cdot t^{47}+\frac{7660305232483900787}{68719476736}\cdot t^{45}-\frac{1791143641983717945}{68719476736}\cdot t^{43}+\frac{11980760805268868921}{2199023255552}\cdot t^{41}-\frac{1115881856010957805}{1099511627776}\cdot t^{39}+\frac{23624813008689135243}{140737488355328}\cdot t^{37}-\frac{3455012179136355747}{140737488355328}\cdot t^{35}+\frac{7113260368810144185}{2251799813685248}\cdot t^{33}-\frac{100101318622914609}{281474976710656}\cdot t^{31}+\frac{156724286732846105}{4503599627370496}\cdot t^{29}-\frac{13228702788676823}{4503599627370496}\cdot t^{27}+\frac{244382877832924467}{1152921504606846976}\cdot t^{25}-\frac{7459794805644825}{576460752303423488}\cdot t^{23}+\frac{12176310231149295}{18446744073709551616}\cdot t^{21}-\frac{511200549488475}{18446744073709551616}\cdot t^{19}+\frac{277508869722315}{295147905179352825856}\cdot t^{17}-\frac{1859539134915}{73786976294838206464}\cdot t^{15}+\frac{612074009925}{1180591620717411303424}\cdot t^{13}-\frac{9306388455}{1180591620717411303424}\cdot t^{11}+\frac{3179201025}{37778931862957161709568}\cdot t^9-\frac{11068785}{18889465931478580854784}\cdot t^7+\frac{2869685}{1208925819614629174706176}\cdot t^5-\frac{5525}{1208925819614629174706176}\cdot t^3+\frac{51}{19342813113834066795298816}\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.