Rule: Q[2, 48, 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.

• $P_1$:
  $4\cdot t^2-1$
• $P_2$:
  $4\cdot t^{50}-49\cdot t^{48}+282\cdot t^{46}-\frac{16215}{16}\cdot t^{44}+\frac{163185}{64}\cdot t^{42}-\frac{1221759}{256}\cdot t^{40}+\frac{1764763}{256}\cdot t^{38}-\frac{16112057}{2048}\cdot t^{36}+\frac{118030185}{16384}\cdot t^{34}-\frac{350343565}{65536}\cdot t^{32}+\frac{52978783}{16384}\cdot t^{30}-\frac{419014011}{262144}\cdot t^{28}+\frac{676868787}{1048576}\cdot t^{26}-\frac{890616825}{4194304}\cdot t^{24}+\frac{237268575}{4194304}\cdot t^{22}-\frac{405992895}{33554432}\cdot t^{20}+\frac{1101980715}{536870912}\cdot t^{18}-\frac{583401555}{2147483648}\cdot t^{16}+\frac{29464725}{1073741824}\cdot t^{14}-\frac{141120525}{68719476736}\cdot t^{12}+\frac{30045015}{274877906944}\cdot t^{10}-\frac{4292145}{1099511627776}\cdot t^8+\frac{94185}{1099511627776}\cdot t^6-\frac{8775}{8796093022208}\cdot t^4+\frac{325}{70368744177664}\cdot t^2-\frac{1}{281474976710656}$
• $P_3$:
  $4\cdot t^{101}-100\cdot t^{99}+\frac{4851}{4}\cdot t^{97}-9506\cdot t^{95}+\frac{433105}{8}\cdot t^{93}-\frac{1910127}{8}\cdot t^{91}+\frac{869107785}{1024}\cdot t^{89}-\frac{1279483491}{512}\cdot t^{87}+\frac{101841441273}{16384}\cdot t^{85}-\frac{217188736765}{16384}\cdot t^{83}+\frac{6426898010533}{262144}\cdot t^{81}-\frac{2600293400865}{65536}\cdot t^{79}+\frac{59344473837519}{1048576}\cdot t^{77}-\frac{75039727938021}{1048576}\cdot t^{75}+\frac{2704353831532575}{33554432}\cdot t^{73}-\frac{1361502273806055}{16777216}\cdot t^{71}+\frac{78682166288559225}{1073741824}\cdot t^{69}-\frac{63871405575418665}{1073741824}\cdot t^{67}+\frac{747194062048945335}{17179869184}\cdot t^{65}-\frac{30797472437020575}{1073741824}\cdot t^{63}+\frac{293402261802444795}{17179869184}\cdot t^{61}-\frac{157826613491614925}{17179869184}\cdot t^{59}+\frac{4909842466984602485}{1099511627776}\cdot t^{57}-\frac{1078165737108891795}{549755813888}\cdot t^{55}+\frac{13684411278689780475}{17592186044416}\cdot t^{53}-\frac{4897952920008965583}{17592186044416}\cdot t^{51}+\frac{25282955356321583475}{281474976710656}\cdot t^{49}-\frac{1835355277718159393}{70368744177664}\cdot t^{47}+\frac{7660305232483900787}{1125899906842624}\cdot t^{45}-\frac{1791143641983717945}{1125899906842624}\cdot t^{43}+\frac{11980760805268868921}{36028797018963968}\cdot t^{41}-\frac{1115881856010957805}{18014398509481984}\cdot t^{39}+\frac{23624813008689135243}{2305843009213693952}\cdot t^{37}-\frac{3455012179136355747}{2305843009213693952}\cdot t^{35}+\frac{7113260368810144185}{36893488147419103232}\cdot t^{33}-\frac{100101318622914609}{4611686018427387904}\cdot t^{31}+\frac{156724286732846105}{73786976294838206464}\cdot t^{29}-\frac{13228702788676823}{73786976294838206464}\cdot t^{27}+\frac{244382877832924467}{18889465931478580854784}\cdot t^{25}-\frac{7459794805644825}{9444732965739290427392}\cdot t^{23}+\frac{12176310231149295}{302231454903657293676544}\cdot t^{21}-\frac{511200549488475}{302231454903657293676544}\cdot t^{19}+\frac{277508869722315}{4835703278458516698824704}\cdot t^{17}-\frac{1859539134915}{1208925819614629174706176}\cdot t^{15}+\frac{612074009925}{19342813113834066795298816}\cdot t^{13}-\frac{9306388455}{19342813113834066795298816}\cdot t^{11}+\frac{3179201025}{618970019642690137449562112}\cdot t^9-\frac{11068785}{309485009821345068724781056}\cdot t^7+\frac{2869685}{19807040628566084398385987584}\cdot t^5-\frac{5525}{19807040628566084398385987584}\cdot t^3+\frac{51}{316912650057057350374175801344}\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.