Rule: Q[18, 95]

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.

• $P_1$:
  $262144\cdot t^{18}-1114112\cdot t^{16}+1966080\cdot t^{14}-1863680\cdot t^{12}+1025024\cdot t^{10}-329472\cdot t^8+59136\cdot t^6-5280\cdot t^4+180\cdot t^2-1$
• $P_2$:
  $262144\cdot t^{113}-7340032\cdot t^{111}+100024320\cdot t^{109}-883998720\cdot t^{107}+5696769024\cdot t^{105}-28536109056\cdot t^{103}+115663719808\cdot t^{101}-389921084800\cdot t^{99}+1115275461300\cdot t^{97}-2747472247520\cdot t^{95}+5897819031335\cdot t^{93}-11134540960305\cdot t^{91}+\frac{298012713937575}{16}\cdot t^{89}-\frac{222204453118725}{8}\cdot t^{87}+\frac{4750096337812287}{128}\cdot t^{85}-\frac{5709711759592547}{128}\cdot t^{83}+\frac{396533655467213009}{8192}\cdot t^{81}-\frac{97390012410079605}{2048}\cdot t^{79}+\frac{11113282527239083815}{262144}\cdot t^{77}-\frac{9007607943130625829}{262144}\cdot t^{75}+\frac{106366434222074411385}{4194304}\cdot t^{73}-\frac{35782256673785401065}{2097152}\cdot t^{71}+\frac{351458133732635263425}{33554432}\cdot t^{69}-\frac{196971041982026356425}{33554432}\cdot t^{67}+\frac{3225947954238964993005}{1073741824}\cdot t^{65}-\frac{94241176191250662717}{67108864}\cdot t^{63}+\frac{1287084035674912897107}{2147483648}\cdot t^{61}-\frac{501354573283331332845}{2147483648}\cdot t^{59}+\frac{2849892607600597709295}{34359738368}\cdot t^{57}-\frac{461301075226222509537}{17179869184}\cdot t^{55}+\frac{2174705068923620402103}{274877906944}\cdot t^{53}-\frac{582344264472745610979}{274877906944}\cdot t^{51}+\frac{18109486273237820829225}{35184372088832}\cdot t^{49}-\frac{995920120525985657275}{8796093022208}\cdot t^{47}+\frac{12665760591630476417815}{562949953421312}\cdot t^{45}-\frac{2267468894342526519645}{562949953421312}\cdot t^{43}+\frac{5833402882026499849685}{9007199254740992}\cdot t^{41}-\frac{419742924119140915825}{4503599627370496}\cdot t^{39}+\frac{861577581086657669325}{72057594037927936}\cdot t^{37}-\frac{98087293846788719277}{72057594037927936}\cdot t^{35}+\frac{315469945074806961999}{2305843009213693952}\cdot t^{33}-\frac{3478285395078058719}{288230376151711744}\cdot t^{31}+\frac{8557686289477763515}{9223372036854775808}\cdot t^{29}-\frac{569017463728786765}{9223372036854775808}\cdot t^{27}+\frac{518766570828062739}{147573952589676412928}\cdot t^{25}-\frac{12530593498262385}{73786976294838206464}\cdot t^{23}+\frac{8108031087110955}{1180591620717411303424}\cdot t^{21}-\frac{270353529420975}{1180591620717411303424}\cdot t^{19}+\frac{466974278090775}{75557863725914323419136}\cdot t^{17}-\frac{2492484372855}{18889465931478580854784}\cdot t^{15}+\frac{10468434365991}{4835703278458516698824704}\cdot t^{13}-\frac{127067830773}{4835703278458516698824704}\cdot t^{11}+\frac{17341763505}{77371252455336267181195264}\cdot t^9-\frac{48275865}{38685626227668133590597632}\cdot t^7+\frac{2503193}{618970019642690137449562112}\cdot t^5-\frac{3857}{618970019642690137449562112}\cdot t^3+\frac{57}{19807040628566084398385987584}\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.