Rule: Q[4, 20, 100]

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.

• $P_1$:
  $16\cdot t^4-12\cdot t^2+1$
• $P_2$:
  $16\cdot t^{24}-92\cdot t^{22}+231\cdot t^{20}-\frac{665}{2}\cdot t^{18}+\frac{4845}{16}\cdot t^{16}-\frac{2907}{16}\cdot t^{14}+\frac{4641}{64}\cdot t^{12}-\frac{2431}{128}\cdot t^{10}+\frac{6435}{2048}\cdot t^8-\frac{5005}{16384}\cdot t^6+\frac{1001}{65536}\cdot t^4-\frac{39}{131072}\cdot t^2+\frac{1}{1048576}$
• $P_3$:
  $16\cdot t^{124}-492\cdot t^{122}+7381\cdot t^{120}-71995\cdot t^{118}+\frac{4107285}{8}\cdot t^{116}-\frac{182637273}{64}\cdot t^{114}+\frac{3295144749}{256}\cdot t^{112}-\frac{6199340121}{128}\cdot t^{110}+\frac{317649948935}{2048}\cdot t^{108}-\frac{3516056331315}{8192}\cdot t^{106}+\frac{34029310406553}{32768}\cdot t^{104}-\frac{72671844711921}{32768}\cdot t^{102}+\frac{1104226171419189}{262144}\cdot t^{100}-\frac{30032524991895525}{4194304}\cdot t^{98}+\frac{183712472698171725}{16777216}\cdot t^{96}-\frac{63464308750277505}{4194304}\cdot t^{94}+\frac{2544977005022596095}{134217728}\cdot t^{92}-\frac{11604873358414583065}{536870912}\cdot t^{90}+\frac{48263258359761583775}{2147483648}\cdot t^{88}-\frac{45866870159177592525}{2147483648}\cdot t^{86}+\frac{319320781774845906055}{17179869184}\cdot t^{84}-\frac{2038740375947093092505}{137438953472}\cdot t^{82}+\frac{5975866538852865101685}{549755813888}\cdot t^{80}-\frac{2012333574464519791275}{274877906944}\cdot t^{78}+\frac{19944018891475092188775}{4398046511104}\cdot t^{76}-\frac{45472363072563210190407}{17592186044416}\cdot t^{74}+\frac{95431897947935688208461}{70368744177664}\cdot t^{72}-\frac{46092957512268257570073}{70368744177664}\cdot t^{70}+\frac{163938869502397410945105}{562949953421312}\cdot t^{68}-\frac{2146280142106099437545685}{18014398509481984}\cdot t^{66}+\frac{3230716424433391784937189}{72057594037927936}\cdot t^{64}-\frac{139694670377010077179851}{9007199254740992}\cdot t^{62}+\frac{2840458297665871569323637}{576460752303423488}\cdot t^{60}-\frac{3311996829294198074903055}{2305843009213693952}\cdot t^{58}+\frac{3538933910034459869304945}{9223372036854775808}\cdot t^{56}-\frac{865072733563979079163431}{9223372036854775808}\cdot t^{54}+\frac{1545467018389580602100961}{73786976294838206464}\cdot t^{52}-\frac{2517554381307842602439649}{590295810358705651712}\cdot t^{50}+\frac{1865701220267457463997925}{2361183241434822606848}\cdot t^{48}-\frac{156865755550215564951525}{1180591620717411303424}\cdot t^{46}+\frac{382014251751701434646655}{18889465931478580854784}\cdot t^{44}-\frac{209863810776486386280915}{75557863725914323419136}\cdot t^{42}+\frac{103667665564288455873705}{302231454903657293676544}\cdot t^{40}-\frac{11466361194008082186825}{302231454903657293676544}\cdot t^{38}+\frac{9046971851164626012725}{2417851639229258349412352}\cdot t^{36}-\frac{12665760591630476417815}{38685626227668133590597632}\cdot t^{34}+\frac{3910562296040009504895}{154742504910672534362390528}\cdot t^{32}-\frac{66136078110878502265}{38685626227668133590597632}\cdot t^{30}+\frac{124541965273732244525}{1237940039285380274899124224}\cdot t^{28}-\frac{25282955356321583475}{4951760157141521099596496896}\cdot t^{26}+\frac{4382378928429074469}{19807040628566084398385987584}\cdot t^{24}-\frac{160245970355912103}{19807040628566084398385987584}\cdot t^{22}+\frac{39006131877993357}{158456325028528675187087900672}\cdot t^{20}-\frac{7768516831046895}{1267650600228229401496703205376}\cdot t^{18}+\frac{620022470083555}{5070602400912917605986812821504}\cdot t^{16}-\frac{4831343922729}{2535301200456458802993406410752}\cdot t^{14}+\frac{910253202833}{40564819207303340847894502572032}\cdot t^{12}-\frac{30999335081}{162259276829213363391578010288128}\cdot t^{10}+\frac{717946515}{649037107316853453566312041152512}\cdot t^8-\frac{2581215}{649037107316853453566312041152512}\cdot t^6+\frac{39711}{5192296858534827628530496329220096}\cdot t^4-\frac{1953}{332306998946228968225951765070086144}\cdot t^2+\frac{1}{1329227995784915872903807060280344576}$

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.