Rule: Q[3, 12, 96]

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.

• $P_1$:
  $8\cdot t^3-4\cdot t$
• $P_2$:
  $8\cdot t^{15}-28\cdot t^{13}+39\cdot t^{11}-\frac{55}{2}\cdot t^9+\frac{165}{16}\cdot t^7-\frac{63}{32}\cdot t^5+\frac{21}{128}\cdot t^3-\frac{1}{256}\cdot t$
• $P_3$:
  $8\cdot t^{111}-220\cdot t^{109}+2943\cdot t^{107}-\frac{51039}{2}\cdot t^{105}+\frac{2580305}{16}\cdot t^{103}-\frac{25335219}{32}\cdot t^{101}+\frac{402336025}{128}\cdot t^{99}-\frac{2655417765}{256}\cdot t^{97}+\frac{59440505355}{2048}\cdot t^{95}-\frac{286301894725}{4096}\cdot t^{93}+\frac{2401567658105}{16384}\cdot t^{91}-\frac{8851862790225}{32768}\cdot t^{89}+\frac{115546315621737}{262144}\cdot t^{87}-\frac{335865397623091}{524288}\cdot t^{85}+\frac{1747870946814045}{2097152}\cdot t^{83}-\frac{4087975829558897}{4194304}\cdot t^{81}+\frac{551876736990451095}{536870912}\cdot t^{79}-\frac{1052837292054228993}{1073741824}\cdot t^{77}+\frac{3641373423818763633}{4294967296}\cdot t^{75}-\frac{5718625495810452225}{8589934592}\cdot t^{73}+\frac{32670756093456235755}{68719476736}\cdot t^{71}-\frac{42483950231417449425}{137438953472}\cdot t^{69}+\frac{100674088124146804395}{549755813888}\cdot t^{67}-\frac{108739818682212303135}{1099511627776}\cdot t^{65}+\frac{214184491343751506175}{4398046511104}\cdot t^{63}-\frac{192322901882458248993}{8796093022208}\cdot t^{61}+\frac{314804034387208046205}{35184372088832}\cdot t^{59}-\frac{234697038272990399589}{70368744177664}\cdot t^{57}+\frac{637034818169545370313}{562949953421312}\cdot t^{55}-\frac{393018988359690434115}{1125899906842624}\cdot t^{53}+\frac{440309078015978388789}{4503599627370496}\cdot t^{51}-\frac{223573904607874331225}{9007199254740992}\cdot t^{49}+\frac{6573072795471505338015}{1152921504606846976}\cdot t^{47}-\frac{2725543418452127836745}{2305843009213693952}\cdot t^{45}+\frac{2034907982102267389425}{9223372036854775808}\cdot t^{43}-\frac{681826310886214268145}{18446744073709551616}\cdot t^{41}+\frac{817394115389905993975}{147573952589676412928}\cdot t^{39}-\frac{218266320541953276229}{295147905179352825856}\cdot t^{37}+\frac{103389309730398920319}{1180591620717411303424}\cdot t^{35}-\frac{21607530484575819315}{2361183241434822606848}\cdot t^{33}+\frac{15845522355355600831}{18889465931478580854784}\cdot t^{31}-\frac{2531146649000465265}{37778931862957161709568}\cdot t^{29}+\frac{699078598295366597}{151115727451828646838272}\cdot t^{27}-\frac{82701917088531741}{302231454903657293676544}\cdot t^{25}+\frac{33169218083635725}{2417851639229258349412352}\cdot t^{23}-\frac{2783353955276895}{4835703278458516698824704}\cdot t^{21}+\frac{385048966145025}{19342813113834066795298816}\cdot t^{19}-\frac{21552658988805}{38685626227668133590597632}\cdot t^{17}+\frac{122131734269895}{9903520314283042199192993792}\cdot t^{15}-\frac{4154140621425}{19807040628566084398385987584}\cdot t^{13}+\frac{209047076433}{79228162514264337593543950336}\cdot t^{11}-\frac{3695785665}{158456325028528675187087900672}\cdot t^9+\frac{170574723}{1267650600228229401496703205376}\cdot t^7-\frac{1145529}{2535301200456458802993406410752}\cdot t^5+\frac{7315}{10141204801825835211973625643008}\cdot t^3-\frac{7}{20282409603651670423947251286016}\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.