Rule: Q[12, 65, 78]

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.

• $P_1$:
  $4096\cdot t^{12}-11264\cdot t^{10}+11520\cdot t^8-5376\cdot t^6+1120\cdot t^4-84\cdot t^2+1$
• $P_2$:
  $4096\cdot t^{77}-77824\cdot t^{75}+710400\cdot t^{73}-4148736\cdot t^{71}+17414880\cdot t^{69}-55966176\cdot t^{67}+143218999\cdot t^{65}-299693680\cdot t^{63}+\frac{1045181709}{2}\cdot t^{61}-\frac{1540002035}{2}\cdot t^{59}+\frac{30999335081}{32}\cdot t^{57}-\frac{16782543687}{16}\cdot t^{55}+\frac{251738155305}{256}\cdot t^{53}-\frac{205263418941}{256}\cdot t^{51}+\frac{37387265592825}{65536}\cdot t^{49}-\frac{5815796869995}{16384}\cdot t^{47}+\frac{202802465047245}{1048576}\cdot t^{45}-\frac{96805419670575}{1048576}\cdot t^{43}+\frac{647520696018735}{16777216}\cdot t^{41}-\frac{118413686604675}{8388608}\cdot t^{39}+\frac{605134770855615}{134217728}\cdot t^{37}-\frac{168345763320735}{134217728}\cdot t^{35}+\frac{1300853625660225}{4294967296}\cdot t^{33}-\frac{33935311973745}{536870912}\cdot t^{31}+\frac{194813827997425}{17179869184}\cdot t^{29}-\frac{29846948742247}{17179869184}\cdot t^{27}+\frac{61989816618513}{274877906944}\cdot t^{25}-\frac{3376351667675}{137438953472}\cdot t^{23}+\frac{4881239839553}{2199023255552}\cdot t^{21}-\frac{360682746765}{2199023255552}\cdot t^{19}+\frac{1370594437707}{140737488355328}\cdot t^{17}-\frac{15991836267}{35184372088832}\cdot t^{15}+\frac{73006209045}{4503599627370496}\cdot t^{13}-\frac{1917334783}{4503599627370496}\cdot t^{11}+\frac{563921995}{72057594037927936}\cdot t^9-\frac{3372291}{36028797018963968}\cdot t^7+\frac{374699}{576460752303423488}\cdot t^5-\frac{1235}{576460752303423488}\cdot t^3+\frac{39}{18446744073709551616}\cdot t$
• $P_3$:
  $4096\cdot t^{155}-157696\cdot t^{153}+2976768\cdot t^{151}-36723200\cdot t^{149}+332985200\cdot t^{147}-2366400120\cdot t^{145}+13725120696\cdot t^{143}-66803044308\cdot t^{141}+\frac{2227520430135}{8}\cdot t^{139}-\frac{16148260351795}{16}\cdot t^{137}+\frac{103039173587207}{32}\cdot t^{135}-\frac{584319326079177}{64}\cdot t^{133}+\frac{94984352672648439}{4096}\cdot t^{131}-\frac{435068188815277815}{8192}\cdot t^{129}+\frac{112925143575796455}{1024}\cdot t^{127}-\frac{427193415484608717}{2048}\cdot t^{125}+\frac{47296413857224536525}{131072}\cdot t^{123}-\frac{150175621316443376025}{262144}\cdot t^{121}+\frac{438919086456271702875}{524288}\cdot t^{119}-\frac{1183884328086624520125}{1048576}\cdot t^{117}+\frac{47257876767034317609225}{33554432}\cdot t^{115}-\frac{109268212419015856059425}{67108864}\cdot t^{113}+\frac{117274295825565186082775}{67108864}\cdot t^{111}-\frac{234050204646968114101125}{134217728}\cdot t^{109}+\frac{6957674265414415755551625}{4294967296}\cdot t^{107}-\frac{12047930002798519618239165}{8589934592}\cdot t^{105}+\frac{19462040773751454767924805}{17179869184}\cdot t^{103}-\frac{29352311278930919292537755}{34359738368}\cdot t^{101}+\frac{10587797997042938744808261625}{17592186044416}\cdot t^{99}-\frac{13945535727302551140663827625}{35184372088832}\cdot t^{97}+\frac{4294339573169357017918702475}{17592186044416}\cdot t^{95}-\frac{4948187404955142989679227497}{35184372088832}\cdot t^{93}+\frac{341424930941904866287866697293}{4503599627370496}\cdot t^{91}-\frac{344453089974649033616362189065}{9007199254740992}\cdot t^{89}+\frac{325187632676163359605032384855}{18014398509481984}\cdot t^{87}-\frac{287255474342745484836464262513}{36028797018963968}\cdot t^{85}+\frac{3798155716309634743948805248783}{1152921504606846976}\cdot t^{83}-\frac{2935526664229317972668131787783}{2305843009213693952}\cdot t^{81}+\frac{1060560480832179999046024419315}{2305843009213693952}\cdot t^{79}-\frac{716104940049078802774666060905}{4611686018427387904}\cdot t^{77}+\frac{7225251912357257161788527221407}{147573952589676412928}\cdot t^{75}-\frac{4252401708757452518337892479195}{295147905179352825856}\cdot t^{73}+\frac{2334024998039804765704256774295}{590295810358705651712}\cdot t^{71}-\frac{1193671973683662243831051262425}{1180591620717411303424}\cdot t^{69}+\frac{18184119806895270285893806893825}{75557863725914323419136}\cdot t^{67}-\frac{8049066845454543063485727135585}{151115727451828646838272}\cdot t^{65}+\frac{413588414983830275989385188785}{37778931862957161709568}\cdot t^{63}-\frac{157668978033070569784749028635}{75557863725914323419136}\cdot t^{61}+\frac{1781075492595797177198090879025}{4835703278458516698824704}\cdot t^{59}-\frac{581235965636354943769966334925}{9671406556917033397649408}\cdot t^{57}+\frac{175028792670872167972993635951}{19342813113834066795298816}\cdot t^{55}-\frac{48537396286880517168981428457}{38685626227668133590597632}\cdot t^{53}+\frac{197883231015743646919693516017}{1237940039285380274899124224}\cdot t^{51}-\frac{46217460990121478260232502825}{2475880078570760549798248448}\cdot t^{49}+\frac{4933890171058719901419156075}{2475880078570760549798248448}\cdot t^{47}-\frac{960132362720877806198759265}{4951760157141521099596496896}\cdot t^{45}+\frac{2715802968839054366105061921}{158456325028528675187087900672}\cdot t^{43}-\frac{434586227336818375437333141}{316912650057057350374175801344}\cdot t^{41}+\frac{62695409292081468659150805}{633825300114114700748351602688}\cdot t^{39}-\frac{8117647787075374502259435}{1267650600228229401496703205376}\cdot t^{37}+\frac{60070593624357771316719819}{162259276829213363391578010288128}\cdot t^{35}-\frac{6167731355736475225789179}{324518553658426726783156020576256}\cdot t^{33}+\frac{139694670377010077179851}{162259276829213363391578010288128}\cdot t^{31}-\frac{11086878601350006125385}{324518553658426726783156020576256}\cdot t^{29}+\frac{97853754611915271454485}{83076749736557242056487941267521536}\cdot t^{27}-\frac{5806706317630136987409}{166153499473114484112975882535043072}\cdot t^{25}+\frac{293267995839905908455}{332306998946228968225951765070086144}\cdot t^{23}-\frac{12442864824332751105}{664613997892457936451903530140172288}\cdot t^{21}+\frac{6986635329170796075}{21267647932558653966460912964485513216}\cdot t^{19}-\frac{199019597082826275}{42535295865117307932921825928971026432}\cdot t^{17}+\frac{2248061893958835}{42535295865117307932921825928971026432}\cdot t^{15}-\frac{39112924418505}{85070591730234615865843651857942052864}\cdot t^{13}+\frac{8070920911755}{2722258935367507707706996859454145691648}\cdot t^{11}-\frac{73263021975}{5444517870735015415413993718908291383296}\cdot t^9+\frac{434652075}{10889035741470030830827987437816582766592}\cdot t^7-\frac{1502501}{21778071482940061661655974875633165533184}\cdot t^5+\frac{79079}{1393796574908163946345982392040522594123776}\cdot t^3-\frac{39}{2787593149816327892691964784081045188247552}\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.