Rule: Q[5, 78, 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.

• $P_1$:
  $32\cdot t^5-32\cdot t^3+6\cdot t$
• $P_2$:
  $32\cdot t^{83}-656\cdot t^{81}+6480\cdot t^{79}-41080\cdot t^{77}+\frac{1502501}{8}\cdot t^{75}-\frac{10555545}{16}\cdot t^{73}+\frac{59273445}{32}\cdot t^{71}-\frac{273273675}{64}\cdot t^{69}+\frac{16871053725}{2048}\cdot t^{67}-\frac{55262073757}{4096}\cdot t^{65}+\frac{19416404293}{1024}\cdot t^{63}-\frac{47223209943}{2048}\cdot t^{61}+\frac{1600342114735}{65536}\cdot t^{59}-\frac{2966614689395}{131072}\cdot t^{57}+\frac{4831343922729}{262144}\cdot t^{55}-\frac{6931928236959}{524288}\cdot t^{53}+\frac{280946973839103}{33554432}\cdot t^{51}-\frac{314492881163175}{67108864}\cdot t^{49}+\frac{155658092696925}{67108864}\cdot t^{47}-\frac{136248095712855}{134217728}\cdot t^{45}+\frac{13488561475572645}{34359738368}\cdot t^{43}-\frac{9206478467454345}{68719476736}\cdot t^{41}+\frac{5534686468704225}{137438953472}\cdot t^{39}-\frac{2923166552608575}{274877906944}\cdot t^{37}+\frac{21631432489303455}{8796093022208}\cdot t^{35}-\frac{8725899885515631}{17592186044416}\cdot t^{33}+\frac{763805560270599}{8796093022208}\cdot t^{31}-\frac{230779457781565}{17592186044416}\cdot t^{29}+\frac{956086325095055}{562949953421312}\cdot t^{27}-\frac{210398934237219}{1125899906842624}\cdot t^{25}+\frac{38962765599485}{2251799813685248}\cdot t^{23}-\frac{5999744185435}{4503599627370496}\cdot t^{21}+\frac{48459472266975}{576460752303423488}\cdot t^{19}-\frac{4923689695575}{1152921504606846976}\cdot t^{17}+\frac{196947587823}{1152921504606846976}\cdot t^{15}-\frac{12058015581}{2305843009213693952}\cdot t^{13}+\frac{17417133617}{147573952589676412928}\cdot t^{11}-\frac{550858165}{295147905179352825856}\cdot t^9+\frac{11344905}{590295810358705651712}\cdot t^7-\frac{135751}{1180591620717411303424}\cdot t^5+\frac{12341}{37778931862957161709568}\cdot t^3-\frac{21}{75557863725914323419136}\cdot t$
• $P_3$:
  $32\cdot t^{167}-1328\cdot t^{165}+27060\cdot t^{163}-360882\cdot t^{161}+3542805\cdot t^{159}-\frac{54602667}{2}\cdot t^{157}+\frac{1375852387}{8}\cdot t^{155}-\frac{14570362235}{16}\cdot t^{153}+\frac{8471208603429}{2048}\cdot t^{151}-\frac{67041535593175}{4096}\cdot t^{149}+\frac{935696166392845}{16384}\cdot t^{147}-\frac{5814102815032785}{32768}\cdot t^{145}+\frac{64849608321519525}{131072}\cdot t^{143}-\frac{326758349026495155}{262144}\cdot t^{141}+\frac{2991748520307520575}{1048576}\cdot t^{139}-\frac{12502771267219795135}{2097152}\cdot t^{137}+\frac{1532576541123942256285}{134217728}\cdot t^{135}-\frac{5400138221451522285975}{268435456}\cdot t^{133}+\frac{35112898746593676019473}{1073741824}\cdot t^{131}-\frac{105611562284438414449245}{2147483648}\cdot t^{129}+\frac{73642656944284083588933}{1073741824}\cdot t^{127}-\frac{190869743508654665628459}{2147483648}\cdot t^{125}+\frac{921071302734790571992875}{8589934592}\cdot t^{123}-\frac{2072203293678900648174675}{17179869184}\cdot t^{121}+\frac{139298110297303876905075375}{1099511627776}\cdot t^{119}-\frac{273569799271991753776373205}{2199023255552}\cdot t^{117}+\frac{1005657994506899263882160655}{8796093022208}\cdot t^{115}-\frac{1731570305750650032767944075}{17592186044416}\cdot t^{113}+\frac{5590498415709241534365076585}{70368744177664}\cdot t^{111}-\frac{8466879887845427826171866175}{140737488355328}\cdot t^{109}+\frac{24075388898482216514419132515}{562949953421312}\cdot t^{107}-\frac{32147758522084447810989145395}{1125899906842624}\cdot t^{105}+\frac{2581275904861486544823540203775}{144115188075855872}\cdot t^{103}-\frac{3043645864924217468004053129165}{288230376151711744}\cdot t^{101}+\frac{6747327312496619057691162555875}{1152921504606846976}\cdot t^{99}-\frac{7031425304601739860120264137175}{2305843009213693952}\cdot t^{97}+\frac{6889376308549179458905713346525}{4611686018427387904}\cdot t^{95}-\frac{6346413290214996138645349719875}{9223372036854775808}\cdot t^{93}+\frac{10991885042728645134058625952075}{36893488147419103232}\cdot t^{91}-\frac{8946883174314013481210509495875}{73786976294838206464}\cdot t^{89}+\frac{1751799725530683839621017759292325}{37778931862957161709568}\cdot t^{87}-\frac{1258590891724656855007149498273975}{75557863725914323419136}\cdot t^{85}+\frac{1698098822168187820247741386560125}{302231454903657293676544}\cdot t^{83}-\frac{1075094007783877795777314221109601}{604462909807314587353088}\cdot t^{81}+\frac{1276871182265309405541971435628705}{2417851639229258349412352}\cdot t^{79}-\frac{710757021239280628450734235442103}{4835703278458516698824704}\cdot t^{77}+\frac{741152902404182152119332991056163}{19342813113834066795298816}\cdot t^{75}-\frac{361649253415088002836495349073475}{38685626227668133590597632}\cdot t^{73}+\frac{5280079099860284841412832096472735}{2475880078570760549798248448}\cdot t^{71}-\frac{2250213782053302663507269380849725}{4951760157141521099596496896}\cdot t^{69}+\frac{1789492044982050185962052192363883}{19807040628566084398385987584}\cdot t^{67}-\frac{663074729588622919584732260317839}{39614081257132168796771975168}\cdot t^{65}+\frac{114323229239417744755988320744455}{39614081257132168796771975168}\cdot t^{63}-\frac{36632201264082502954625954128617}{79228162514264337593543950336}\cdot t^{61}+\frac{21779378919191351659183072142745}{316912650057057350374175801344}\cdot t^{59}-\frac{5995899811864264310355951156273}{633825300114114700748351602688}\cdot t^{57}+\frac{48823755610894723670041316558223}{40564819207303340847894502572032}\cdot t^{55}-\frac{11459345200281122909753651823765}{81129638414606681695789005144064}\cdot t^{53}+\frac{4950149744823632404276028906943}{324518553658426726783156020576256}\cdot t^{51}-\frac{981408944899724975190784770075}{649037107316853453566312041152512}\cdot t^{49}+\frac{356215098519159435439618175805}{2596148429267413814265248164610048}\cdot t^{47}-\frac{58996249655157246776501799915}{5192296858534827628530496329220096}\cdot t^{45}+\frac{17774280936885476052567492975}{20769187434139310514121985316880384}\cdot t^{43}-\frac{2426330413606588794477467295}{41538374868278621028243970633760768}\cdot t^{41}+\frac{38261364214565438682144676575}{10633823966279326983230456482242756608}\cdot t^{39}-\frac{4234752932485883504625721485}{21267647932558653966460912964485513216}\cdot t^{37}+\frac{837892291454426147974073235}{85070591730234615865843651857942052864}\cdot t^{35}-\frac{73673106755635223591631975}{170141183460469231731687303715884105728}\cdot t^{33}+\frac{5720500053966970302409071}{340282366920938463463374607431768211456}\cdot t^{31}-\frac{389406020362266313954065}{680564733841876926926749214863536422912}\cdot t^{29}+\frac{46092957512268257570073}{2722258935367507707706996859454145691648}\cdot t^{27}-\frac{2349154651779607725729}{5444517870735015415413993718908291383296}\cdot t^{25}+\frac{6525429588276688127025}{696898287454081973172991196020261297061888}\cdot t^{23}-\frac{238058209925595111195}{1393796574908163946345982392040522594123776}\cdot t^{21}+\frac{14373842462442488025}{5575186299632655785383929568162090376495104}\cdot t^{19}-\frac{352390976498590029}{11150372599265311570767859136324180752990208}\cdot t^{17}+\frac{13708573456466889}{44601490397061246283071436545296723011960832}\cdot t^{15}-\frac{205423178668335}{89202980794122492566142873090593446023921664}\cdot t^{13}+\frac{4564959525963}{356811923176489970264571492362373784095686656}\cdot t^{11}-\frac{35709397515}{713623846352979940529142984724747568191373312}\cdot t^9+\frac{5843355957}{45671926166590716193865151022383844364247891968}\cdot t^7-\frac{17413151}{91343852333181432387730302044767688728495783936}\cdot t^5+\frac{49385}{365375409332725729550921208179070754913983135744}\cdot t^3-\frac{21}{730750818665451459101842416358141509827966271488}\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.