Rule: Q[6, 7, 14, 56, 84]

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.

• $P_1$:
  $64\cdot t^6-80\cdot t^4+24\cdot t^2-1$
• $P_2$:
  $64\cdot t^{13}-192\cdot t^{11}+220\cdot t^9-120\cdot t^7+\frac{63}{2}\cdot t^5-\frac{7}{2}\cdot t^3+\frac{7}{64}\cdot t$
• $P_3$:
  $64\cdot t^{27}-416\cdot t^{25}+1200\cdot t^{23}-2024\cdot t^{21}+\frac{8855}{4}\cdot t^{19}-\frac{13167}{8}\cdot t^{17}+\frac{6783}{8}\cdot t^{15}-\frac{4845}{16}\cdot t^{13}+\frac{37791}{512}\cdot t^{11}-\frac{12155}{1024}\cdot t^9+\frac{2431}{2048}\cdot t^7-\frac{273}{4096}\cdot t^5+\frac{455}{262144}\cdot t^3-\frac{7}{524288}\cdot t$
• $P_4$:
  $64\cdot t^{83}-1312\cdot t^{81}+12960\cdot t^{79}-82160\cdot t^{77}+\frac{1502501}{4}\cdot t^{75}-\frac{10555545}{8}\cdot t^{73}+\frac{59273445}{16}\cdot t^{71}-\frac{273273675}{32}\cdot t^{69}+\frac{16871053725}{1024}\cdot t^{67}-\frac{55262073757}{2048}\cdot t^{65}+\frac{19416404293}{512}\cdot t^{63}-\frac{47223209943}{1024}\cdot t^{61}+\frac{1600342114735}{32768}\cdot t^{59}-\frac{2966614689395}{65536}\cdot t^{57}+\frac{4831343922729}{131072}\cdot t^{55}-\frac{6931928236959}{262144}\cdot t^{53}+\frac{280946973839103}{16777216}\cdot t^{51}-\frac{314492881163175}{33554432}\cdot t^{49}+\frac{155658092696925}{33554432}\cdot t^{47}-\frac{136248095712855}{67108864}\cdot t^{45}+\frac{13488561475572645}{17179869184}\cdot t^{43}-\frac{9206478467454345}{34359738368}\cdot t^{41}+\frac{5534686468704225}{68719476736}\cdot t^{39}-\frac{2923166552608575}{137438953472}\cdot t^{37}+\frac{21631432489303455}{4398046511104}\cdot t^{35}-\frac{8725899885515631}{8796093022208}\cdot t^{33}+\frac{763805560270599}{4398046511104}\cdot t^{31}-\frac{230779457781565}{8796093022208}\cdot t^{29}+\frac{956086325095055}{281474976710656}\cdot t^{27}-\frac{210398934237219}{562949953421312}\cdot t^{25}+\frac{38962765599485}{1125899906842624}\cdot t^{23}-\frac{5999744185435}{2251799813685248}\cdot t^{21}+\frac{48459472266975}{288230376151711744}\cdot t^{19}-\frac{4923689695575}{576460752303423488}\cdot t^{17}+\frac{196947587823}{576460752303423488}\cdot t^{15}-\frac{12058015581}{1152921504606846976}\cdot t^{13}+\frac{17417133617}{73786976294838206464}\cdot t^{11}-\frac{550858165}{147573952589676412928}\cdot t^9+\frac{11344905}{295147905179352825856}\cdot t^7-\frac{135751}{590295810358705651712}\cdot t^5+\frac{12341}{18889465931478580854784}\cdot t^3-\frac{21}{37778931862957161709568}\cdot t$
• $P_5$:
  $64\cdot t^{167}-2656\cdot t^{165}+54120\cdot t^{163}-721764\cdot t^{161}+7085610\cdot t^{159}-54602667\cdot t^{157}+\frac{1375852387}{4}\cdot t^{155}-\frac{14570362235}{8}\cdot t^{153}+\frac{8471208603429}{1024}\cdot t^{151}-\frac{67041535593175}{2048}\cdot t^{149}+\frac{935696166392845}{8192}\cdot t^{147}-\frac{5814102815032785}{16384}\cdot t^{145}+\frac{64849608321519525}{65536}\cdot t^{143}-\frac{326758349026495155}{131072}\cdot t^{141}+\frac{2991748520307520575}{524288}\cdot t^{139}-\frac{12502771267219795135}{1048576}\cdot t^{137}+\frac{1532576541123942256285}{67108864}\cdot t^{135}-\frac{5400138221451522285975}{134217728}\cdot t^{133}+\frac{35112898746593676019473}{536870912}\cdot t^{131}-\frac{105611562284438414449245}{1073741824}\cdot t^{129}+\frac{73642656944284083588933}{536870912}\cdot t^{127}-\frac{190869743508654665628459}{1073741824}\cdot t^{125}+\frac{921071302734790571992875}{4294967296}\cdot t^{123}-\frac{2072203293678900648174675}{8589934592}\cdot t^{121}+\frac{139298110297303876905075375}{549755813888}\cdot t^{119}-\frac{273569799271991753776373205}{1099511627776}\cdot t^{117}+\frac{1005657994506899263882160655}{4398046511104}\cdot t^{115}-\frac{1731570305750650032767944075}{8796093022208}\cdot t^{113}+\frac{5590498415709241534365076585}{35184372088832}\cdot t^{111}-\frac{8466879887845427826171866175}{70368744177664}\cdot t^{109}+\frac{24075388898482216514419132515}{281474976710656}\cdot t^{107}-\frac{32147758522084447810989145395}{562949953421312}\cdot t^{105}+\frac{2581275904861486544823540203775}{72057594037927936}\cdot t^{103}-\frac{3043645864924217468004053129165}{144115188075855872}\cdot t^{101}+\frac{6747327312496619057691162555875}{576460752303423488}\cdot t^{99}-\frac{7031425304601739860120264137175}{1152921504606846976}\cdot t^{97}+\frac{6889376308549179458905713346525}{2305843009213693952}\cdot t^{95}-\frac{6346413290214996138645349719875}{4611686018427387904}\cdot t^{93}+\frac{10991885042728645134058625952075}{18446744073709551616}\cdot t^{91}-\frac{8946883174314013481210509495875}{36893488147419103232}\cdot t^{89}+\frac{1751799725530683839621017759292325}{18889465931478580854784}\cdot t^{87}-\frac{1258590891724656855007149498273975}{37778931862957161709568}\cdot t^{85}+\frac{1698098822168187820247741386560125}{151115727451828646838272}\cdot t^{83}-\frac{1075094007783877795777314221109601}{302231454903657293676544}\cdot t^{81}+\frac{1276871182265309405541971435628705}{1208925819614629174706176}\cdot t^{79}-\frac{710757021239280628450734235442103}{2417851639229258349412352}\cdot t^{77}+\frac{741152902404182152119332991056163}{9671406556917033397649408}\cdot t^{75}-\frac{361649253415088002836495349073475}{19342813113834066795298816}\cdot t^{73}+\frac{5280079099860284841412832096472735}{1237940039285380274899124224}\cdot t^{71}-\frac{2250213782053302663507269380849725}{2475880078570760549798248448}\cdot t^{69}+\frac{1789492044982050185962052192363883}{9903520314283042199192993792}\cdot t^{67}-\frac{663074729588622919584732260317839}{19807040628566084398385987584}\cdot t^{65}+\frac{114323229239417744755988320744455}{19807040628566084398385987584}\cdot t^{63}-\frac{36632201264082502954625954128617}{39614081257132168796771975168}\cdot t^{61}+\frac{21779378919191351659183072142745}{158456325028528675187087900672}\cdot t^{59}-\frac{5995899811864264310355951156273}{316912650057057350374175801344}\cdot t^{57}+\frac{48823755610894723670041316558223}{20282409603651670423947251286016}\cdot t^{55}-\frac{11459345200281122909753651823765}{40564819207303340847894502572032}\cdot t^{53}+\frac{4950149744823632404276028906943}{162259276829213363391578010288128}\cdot t^{51}-\frac{981408944899724975190784770075}{324518553658426726783156020576256}\cdot t^{49}+\frac{356215098519159435439618175805}{1298074214633706907132624082305024}\cdot t^{47}-\frac{58996249655157246776501799915}{2596148429267413814265248164610048}\cdot t^{45}+\frac{17774280936885476052567492975}{10384593717069655257060992658440192}\cdot t^{43}-\frac{2426330413606588794477467295}{20769187434139310514121985316880384}\cdot t^{41}+\frac{38261364214565438682144676575}{5316911983139663491615228241121378304}\cdot t^{39}-\frac{4234752932485883504625721485}{10633823966279326983230456482242756608}\cdot t^{37}+\frac{837892291454426147974073235}{42535295865117307932921825928971026432}\cdot t^{35}-\frac{73673106755635223591631975}{85070591730234615865843651857942052864}\cdot t^{33}+\frac{5720500053966970302409071}{170141183460469231731687303715884105728}\cdot t^{31}-\frac{389406020362266313954065}{340282366920938463463374607431768211456}\cdot t^{29}+\frac{46092957512268257570073}{1361129467683753853853498429727072845824}\cdot t^{27}-\frac{2349154651779607725729}{2722258935367507707706996859454145691648}\cdot t^{25}+\frac{6525429588276688127025}{348449143727040986586495598010130648530944}\cdot t^{23}-\frac{238058209925595111195}{696898287454081973172991196020261297061888}\cdot t^{21}+\frac{14373842462442488025}{2787593149816327892691964784081045188247552}\cdot t^{19}-\frac{352390976498590029}{5575186299632655785383929568162090376495104}\cdot t^{17}+\frac{13708573456466889}{22300745198530623141535718272648361505980416}\cdot t^{15}-\frac{205423178668335}{44601490397061246283071436545296723011960832}\cdot t^{13}+\frac{4564959525963}{178405961588244985132285746181186892047843328}\cdot t^{11}-\frac{35709397515}{356811923176489970264571492362373784095686656}\cdot t^9+\frac{5843355957}{22835963083295358096932575511191922182123945984}\cdot t^7-\frac{17413151}{45671926166590716193865151022383844364247891968}\cdot t^5+\frac{49385}{182687704666362864775460604089535377456991567872}\cdot t^3-\frac{21}{365375409332725729550921208179070754913983135744}\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.