Rule: Q[1, 2, 12, 48, 64]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^3-1\cdot t$
• $P_3$:
  $2\cdot t^{15}-7\cdot t^{13}+\frac{39}{4}\cdot t^{11}-\frac{55}{8}\cdot t^9+\frac{165}{64}\cdot t^7-\frac{63}{128}\cdot t^5+\frac{21}{512}\cdot t^3-\frac{1}{1024}\cdot t$
• $P_4$:
  $2\cdot t^{63}-31\cdot t^{61}+\frac{915}{4}\cdot t^{59}-\frac{8555}{8}\cdot t^{57}+\frac{227563}{64}\cdot t^{55}-\frac{1145529}{128}\cdot t^{53}+\frac{9072063}{512}\cdot t^{51}-\frac{28989675}{1024}\cdot t^{49}+\frac{608783175}{16384}\cdot t^{47}-\frac{1329484065}{32768}\cdot t^{45}+\frac{4874774905}{131072}\cdot t^{43}-\frac{7550466105}{262144}\cdot t^{41}+\frac{39688347475}{2097152}\cdot t^{39}-\frac{44357564825}{4194304}\cdot t^{37}+\frac{84406109067}{16777216}\cdot t^{35}-\frac{68328754959}{33554432}\cdot t^{33}+\frac{751616304549}{1073741824}\cdot t^{31}-\frac{437423756715}{2147483648}\cdot t^{29}+\frac{428971123735}{8589934592}\cdot t^{27}-\frac{176103935007}{17179869184}\cdot t^{25}+\frac{240141729555}{137438953472}\cdot t^{23}-\frac{67282234305}{274877906944}\cdot t^{21}+\frac{30582833775}{1099511627776}\cdot t^{19}-\frac{5545773675}{2199023255552}\cdot t^{17}+\frac{6285210165}{35184372088832}\cdot t^{15}-\frac{676868787}{70368744177664}\cdot t^{13}+\frac{106874019}{281474976710656}\cdot t^{11}-\frac{5883955}{562949953421312}\cdot t^9+\frac{840565}{4503599627370496}\cdot t^7-\frac{17391}{9007199254740992}\cdot t^5+\frac{341}{36028797018963968}\cdot t^3-\frac{1}{72057594037927936}\cdot t$
• $P_5$:
  $2\cdot t^{127}-63\cdot t^{125}+\frac{3875}{4}\cdot t^{123}-\frac{77531}{8}\cdot t^{121}+\frac{4539315}{64}\cdot t^{119}-\frac{51822001}{128}\cdot t^{117}+\frac{960830871}{512}\cdot t^{115}-\frac{7435946115}{1024}\cdot t^{113}+\frac{392122225131}{16384}\cdot t^{111}-\frac{2235206521405}{32768}\cdot t^{109}+\frac{22299026415237}{131072}\cdot t^{107}-\frac{98257792386021}{262144}\cdot t^{105}+\frac{1541630880539295}{2097152}\cdot t^{103}-\frac{5416847501988573}{4194304}\cdot t^{101}+\frac{34279548728123175}{16777216}\cdot t^{99}-\frac{98106248306858715}{33554432}\cdot t^{97}+\frac{4078416893899412295}{1073741824}\cdot t^{95}-\frac{9650308124674550025}{2147483648}\cdot t^{93}+\frac{41701028441775479805}{8589934592}\cdot t^{91}-\frac{82455679125577300725}{17179869184}\cdot t^{89}+\frac{597956369362519832665}{137438953472}\cdot t^{87}-\frac{995529496121578412995}{274877906944}\cdot t^{85}+\frac{3048062007850801830525}{1099511627776}\cdot t^{83}-\frac{4295053835493283076305}{2199023255552}\cdot t^{81}+\frac{44602482137814862715475}{35184372088832}\cdot t^{79}-\frac{53367086394799064864613}{70368744177664}\cdot t^{77}+\frac{117761760777663698185413}{281474976710656}\cdot t^{75}-\frac{119834575048777690672725}{562949953421312}\cdot t^{73}+\frac{449893233183125387268459}{4503599627370496}\cdot t^{71}-\frac{389406020362266313954065}{9007199254740992}\cdot t^{69}+\frac{621460220251616852065467}{36028797018963968}\cdot t^{67}-\frac{456949965738717944767791}{72057594037927936}\cdot t^{65}+\frac{9900582591005555469968805}{4611686018427387904}\cdot t^{63}-\frac{6167731355736475225789179}{9223372036854775808}\cdot t^{61}+\frac{7063171702752033581473215}{36893488147419103232}\cdot t^{59}-\frac{3712776277544924564639223}{73786976294838206464}\cdot t^{57}+\frac{7156510795847463291261111}{590295810358705651712}\cdot t^{55}-\frac{3156346460301004748299005}{1180591620717411303424}\cdot t^{53}+\frac{2543535334675312598336859}{4722366482869645213696}\cdot t^{51}-\frac{934315053791709467841975}{9444732965739290427392}\cdot t^{49}+\frac{2497169325588750759504915}{151115727451828646838272}\cdot t^{47}-\frac{756781620678844847497845}{302231454903657293676544}\cdot t^{45}+\frac{414847067813984717066925}{1208925819614629174706176}\cdot t^{43}-\frac{102491628518749165393005}{2417851639229258349412352}\cdot t^{41}+\frac{90955774226595579677775}{19342813113834066795298816}\cdot t^{39}-\frac{18045041151782416209165}{38685626227668133590597632}\cdot t^{37}+\frac{6372214956037693104615}{154742504910672534362390528}\cdot t^{35}-\frac{995920120525985657275}{309485009821345068724781056}\cdot t^{33}+\frac{2191024265157168446005}{9903520314283042199192993792}\cdot t^{31}-\frac{263194596563700162075}{19807040628566084398385987584}\cdot t^{29}+\frac{54798464720442187591}{79228162514264337593543950336}\cdot t^{27}-\frac{4897952920008965583}{158456325028528675187087900672}\cdot t^{25}+\frac{1487232668018916675}{1267650600228229401496703205376}\cdot t^{23}-\frac{94659085536801489}{2535301200456458802993406410752}\cdot t^{21}+\frac{9949153134498655}{10141204801825835211973625643008}\cdot t^{19}-\frac{423737281693467}{20282409603651670423947251286016}\cdot t^{17}+\frac{114341806171253}{324518553658426726783156020576256}\cdot t^{15}-\frac{2966614689395}{649037107316853453566312041152512}\cdot t^{13}+\frac{113988150627}{2596148429267413814265248164610048}\cdot t^{11}-\frac{1540002035}{5192296858534827628530496329220096}\cdot t^9+\frac{54353013}{41538374868278621028243970633760768}\cdot t^7-\frac{279279}{83076749736557242056487941267521536}\cdot t^5+\frac{1365}{332306998946228968225951765070086144}\cdot t^3-\frac{1}{664613997892457936451903530140172288}\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.