Rule: Q[1, 56, 58]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{57}-28\cdot t^{55}+\frac{1485}{8}\cdot t^{53}-\frac{6201}{8}\cdot t^{51}+\frac{292825}{128}\cdot t^{49}-\frac{162435}{32}\cdot t^{47}+\frac{4502365}{512}\cdot t^{45}-\frac{6242775}{512}\cdot t^{43}+\frac{225489033}{16384}\cdot t^{41}-\frac{104819165}{8192}\cdot t^{39}+\frac{5178066751}{524288}\cdot t^{37}-\frac{3335195799}{524288}\cdot t^{35}+\frac{28760021745}{8388608}\cdot t^{33}-\frac{1622360201}{1048576}\cdot t^{31}+\frac{9797370045}{16777216}\cdot t^{29}-\frac{3083513363}{16777216}\cdot t^{27}+\frac{51538723353}{1073741824}\cdot t^{25}-\frac{5545773675}{536870912}\cdot t^{23}+\frac{31179571995}{17179869184}\cdot t^{21}-\frac{4418157975}{17179869184}\cdot t^{19}+\frac{7952684355}{274877906944}\cdot t^{17}-\frac{173996955}{68719476736}\cdot t^{15}+\frac{184542225}{1099511627776}\cdot t^{13}-\frac{8940555}{1099511627776}\cdot t^{11}+\frac{9641775}{35184372088832}\cdot t^9-\frac{105183}{17592186044416}\cdot t^7+\frac{169911}{2251799813685248}\cdot t^5-\frac{1015}{2251799813685248}\cdot t^3+\frac{29}{36028797018963968}\cdot t$
• $P_3$:
  $2\cdot t^{115}-57\cdot t^{113}+791\cdot t^{111}-\frac{14245}{2}\cdot t^{109}+\frac{5989005}{128}\cdot t^{107}-\frac{61195761}{256}\cdot t^{105}+\frac{506255841}{512}\cdot t^{103}-\frac{3485402271}{1024}\cdot t^{101}+\frac{325949656825}{32768}\cdot t^{99}-\frac{1641933318025}{65536}\cdot t^{97}+\frac{1803028662435}{32768}\cdot t^{95}-\frac{6970149764305}{65536}\cdot t^{93}+\frac{382285906303805}{2097152}\cdot t^{91}-\frac{1169126800832025}{4194304}\cdot t^{89}+\frac{3206092823570175}{8388608}\cdot t^{87}-\frac{7916827229687145}{16777216}\cdot t^{85}+\frac{565261464199662153}{1073741824}\cdot t^{83}-\frac{1142949948111378673}{2147483648}\cdot t^{81}+\frac{1049647911530857965}{2147483648}\cdot t^{79}-\frac{1754728820090381655}{4294967296}\cdot t^{77}+\frac{171144550919481890751}{549755813888}\cdot t^{75}-\frac{238058209925595111195}{1099511627776}\cdot t^{73}+\frac{302522715514731118095}{2199023255552}\cdot t^{71}-\frac{351458133732635263425}{4398046511104}\cdot t^{69}+\frac{5974788273454799478225}{140737488355328}\cdot t^{67}-\frac{5806706317630136987409}{281474976710656}\cdot t^{65}+\frac{645189590847792998601}{70368744177664}\cdot t^{63}-\frac{524367570089779328451}{140737488355328}\cdot t^{61}+\frac{6231121125092832279645}{4503599627370496}\cdot t^{59}-\frac{4225702831959506948265}{9007199254740992}\cdot t^{57}+\frac{2614039426281927554043}{18014398509481984}\cdot t^{55}-\frac{1473187304754710594973}{36028797018963968}\cdot t^{53}+\frac{48334573951237885711257}{4611686018427387904}\cdot t^{51}-\frac{22499664763719716787825}{9223372036854775808}\cdot t^{49}+\frac{4745266456623814014075}{9223372036854775808}\cdot t^{47}-\frac{1809394370232925202545}{18446744073709551616}\cdot t^{45}+\frac{19903338072562177227995}{1180591620717411303424}\cdot t^{43}-\frac{6148721956730634976695}{2361183241434822606848}\cdot t^{41}+\frac{1701063429324939500975}{4722366482869645213696}\cdot t^{39}-\frac{419742924119140915825}{9444732965739290427392}\cdot t^{37}+\frac{1471309407701830789155}{302231454903657293676544}\cdot t^{35}-\frac{284692389457752624243}{604462909807314587353088}\cdot t^{33}+\frac{12091182563842775547}{302231454903657293676544}\cdot t^{31}-\frac{1791143641983717945}{604462909807314587353088}\cdot t^{29}+\frac{3672749084067623665}{19342813113834066795298816}\cdot t^{27}-\frac{403485110644048797}{38685626227668133590597632}\cdot t^{25}+\frac{37591780494787155}{77371252455336267181195264}\cdot t^{23}-\frac{2932692095338005}{154742504910672534362390528}\cdot t^{21}+\frac{6037895490401775}{9903520314283042199192993792}\cdot t^{19}-\frac{314492881163175}{19807040628566084398385987584}\cdot t^{17}+\frac{6480459369423}{19807040628566084398385987584}\cdot t^{15}-\frac{205263418941}{39614081257132168796771975168}\cdot t^{13}+\frac{615790256823}{10141204801825835211973625643008}\cdot t^{11}-\frac{10143295635}{20282409603651670423947251286016}\cdot t^9+\frac{109067695}{40564819207303340847894502572032}\cdot t^7-\frac{682689}{81129638414606681695789005144064}\cdot t^5+\frac{32509}{2596148429267413814265248164610048}\cdot t^3-\frac{29}{5192296858534827628530496329220096}\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.