Rule: Q[2, 12, 90]

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.

• $P_1$:
  $4\cdot t^2-1$
• $P_2$:
  $4\cdot t^{14}-13\cdot t^{12}+\frac{33}{2}\cdot t^{10}-\frac{165}{16}\cdot t^8+\frac{105}{32}\cdot t^6-\frac{63}{128}\cdot t^4+\frac{7}{256}\cdot t^2-\frac{1}{4096}$
• $P_3$:
  $4\cdot t^{104}-103\cdot t^{102}+\frac{5151}{4}\cdot t^{100}-\frac{83325}{8}\cdot t^{98}+\frac{3921225}{64}\cdot t^{96}-\frac{8940393}{32}\cdot t^{94}+\frac{131577299}{128}\cdot t^{92}-\frac{802890049}{256}\cdot t^{90}+\frac{33150254085}{4096}\cdot t^{88}-\frac{1174992339235}{65536}\cdot t^{86}+\frac{9041256841903}{262144}\cdot t^{84}-\frac{30481451983437}{524288}\cdot t^{82}+\frac{362827605867363}{4194304}\cdot t^{80}-\frac{479320750226115}{4194304}\cdot t^{78}+\frac{2259654965351685}{16777216}\cdot t^{76}-\frac{4770382704631335}{33554432}\cdot t^{74}+\frac{144773075114710515}{1073741824}\cdot t^{72}-\frac{494705855605882455}{4294967296}\cdot t^{70}+\frac{1525816910968334775}{17179869184}\cdot t^{68}-\frac{2127179267555609925}{34359738368}\cdot t^{66}+\frac{10735998891545372445}{274877906944}\cdot t^{64}-\frac{1533714127363624635}{68719476736}\cdot t^{62}+\frac{3176619293367594945}{274877906944}\cdot t^{60}-\frac{2981238679353469275}{549755813888}\cdot t^{58}+\frac{20279784102762488525}{8796093022208}\cdot t^{56}-\frac{62461735036508464657}{70368744177664}\cdot t^{54}+\frac{87032855732467003821}{281474976710656}\cdot t^{52}-\frac{54798464720442187591}{562949953421312}\cdot t^{50}+\frac{124541965273732244525}{4503599627370496}\cdot t^{48}-\frac{31870085487470501775}{4503599627370496}\cdot t^{46}+\frac{29320478648472861633}{18014398509481984}\cdot t^{44}-\frac{12091182563842775547}{36028797018963968}\cdot t^{42}+\frac{142609701198200407479}{2305843009213693952}\cdot t^{40}-\frac{93632632099828550365}{9223372036854775808}\cdot t^{38}+\frac{54534996160877772085}{36893488147419103232}\cdot t^{36}-\frac{14023284727082855679}{73786976294838206464}\cdot t^{34}+\frac{12668377990166637739}{590295810358705651712}\cdot t^{32}-\frac{624355672011392321}{295147905179352825856}\cdot t^{30}+\frac{213350131441441995}{1180591620717411303424}\cdot t^{28}-\frac{31331138183708265}{2361183241434822606848}\cdot t^{26}+\frac{31331138183708265}{37778931862957161709568}\cdot t^{24}-\frac{52728013040874885}{1208925819614629174706176}\cdot t^{22}+\frac{9206478467454345}{4835703278458516698824704}\cdot t^{20}-\frac{656125622211675}{9671406556917033397649408}\cdot t^{18}+\frac{149608375854525}{77371252455336267181195264}\cdot t^{16}-\frac{3324630574545}{77371252455336267181195264}\cdot t^{14}+\frac{222948697335}{309485009821345068724781056}\cdot t^{12}-\frac{5397877485}{618970019642690137449562112}\cdot t^{10}+\frac{1420494075}{19807040628566084398385987584}\cdot t^8-\frac{28989675}{79228162514264337593543950336}\cdot t^6+\frac{316251}{316912650057057350374175801344}\cdot t^4-\frac{689}{633825300114114700748351602688}\cdot t^2+\frac{1}{5070602400912917605986812821504}$

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.