Rule: Q[3, 16, 80]

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.

• $P_1$:
  $8\cdot t^3-4\cdot t$
• $P_2$:
  $8\cdot t^{19}-36\cdot t^{17}+68\cdot t^{15}-70\cdot t^{13}+\frac{1365}{32}\cdot t^{11}-\frac{1001}{64}\cdot t^9+\frac{429}{128}\cdot t^7-\frac{99}{256}\cdot t^5+\frac{165}{8192}\cdot t^3-\frac{5}{16384}\cdot t$
• $P_3$:
  $8\cdot t^{99}-196\cdot t^{97}+2328\cdot t^{95}-17860\cdot t^{93}+\frac{3183545}{32}\cdot t^{91}-\frac{27445509}{64}\cdot t^{89}+\frac{190561371}{128}\cdot t^{87}-\frac{1095069261}{256}\cdot t^{85}+\frac{84986896995}{8192}\cdot t^{83}-\frac{353126264315}{16384}\cdot t^{81}+\frac{635627275767}{16384}\cdot t^{79}-\frac{2000375522613}{32768}\cdot t^{77}+\frac{88683314835843}{1048576}\cdot t^{75}-\frac{217591687594575}{2097152}\cdot t^{73}+\frac{474942653653275}{4194304}\cdot t^{71}-\frac{925672544571285}{8388608}\cdot t^{69}+\frac{51705423561053205}{536870912}\cdot t^{67}-\frac{81021042872777205}{1073741824}\cdot t^{65}+\frac{14271999422033925}{268435456}\cdot t^{63}-\frac{18111250728545975}{536870912}\cdot t^{61}+\frac{662871776664782685}{34359738368}\cdot t^{59}-\frac{683648951099121865}{68719476736}\cdot t^{57}+\frac{635841332141141315}{137438953472}\cdot t^{55}-\frac{533158880987913525}{274877906944}\cdot t^{53}+\frac{6444674894748638925}{8796093022208}\cdot t^{51}-\frac{4382378928429074469}{17592186044416}\cdot t^{49}+\frac{1339313310767305503}{17592186044416}\cdot t^{47}-\frac{734549816813524733}{35184372088832}\cdot t^{45}+\frac{5771462846391980045}{1125899906842624}\cdot t^{43}-\frac{2531146649000465265}{2251799813685248}\cdot t^{41}+\frac{988352501038276913}{4503599627370496}\cdot t^{39}-\frac{342388594328828047}{9007199254740992}\cdot t^{37}+\frac{6706788347735278803}{1152921504606846976}\cdot t^{35}-\frac{1804857108504066435}{2305843009213693952}\cdot t^{33}+\frac{106168065206121555}{1152921504606846976}\cdot t^{31}-\frac{21700285855317153}{2305843009213693952}\cdot t^{29}+\frac{489462003181042451}{590295810358705651712}\cdot t^{27}-\frac{73702772679770871}{1180591620717411303424}\cdot t^{25}+\frac{9384903142585425}{2361183241434822606848}\cdot t^{23}-\frac{998058215667975}{4722366482869645213696}\cdot t^{21}+\frac{1397281501935165}{151115727451828646838272}\cdot t^{19}-\frac{98774343460485}{302231454903657293676544}\cdot t^{17}+\frac{2757247682805}{302231454903657293676544}\cdot t^{15}-\frac{118119545775}{604462909807314587353088}\cdot t^{13}+\frac{59826782925}{19342813113834066795298816}\cdot t^{11}-\frac{1329484065}{38685626227668133590597632}\cdot t^9+\frac{19267885}{77371252455336267181195264}\cdot t^7-\frac{162435}{154742504910672534362390528}\cdot t^5+\frac{20825}{9903520314283042199192993792}\cdot t^3-\frac{25}{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.