Rule: Q[8, 90, 99]

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.

• $P_1$:
  $256\cdot t^8-448\cdot t^6+240\cdot t^4-40\cdot t^2+1$
• $P_2$:
  $256\cdot t^{98}-6208\cdot t^{96}+72960\cdot t^{94}-553660\cdot t^{92}+3049501\cdot t^{90}-\frac{51971283}{4}\cdot t^{88}+\frac{178267089}{4}\cdot t^{86}-\frac{4046995095}{32}\cdot t^{84}+\frac{77515521435}{256}\cdot t^{82}-\frac{635627275767}{1024}\cdot t^{80}+\frac{564208480737}{512}\cdot t^{78}-\frac{14002628658291}{8192}\cdot t^{76}+\frac{76451133479175}{32768}\cdot t^{74}-\frac{369399841730325}{131072}\cdot t^{72}+\frac{396716804816265}{131072}\cdot t^{70}-\frac{3041495503591365}{1048576}\cdot t^{68}+\frac{41738112995067045}{16777216}\cdot t^{66}-\frac{128447994798305325}{67108864}\cdot t^{64}+\frac{11100443994915275}{8388608}\cdot t^{62}-\frac{220957258888260895}{268435456}\cdot t^{60}+\frac{495056137002812385}{1073741824}\cdot t^{58}-\frac{999179236221793495}{4294967296}\cdot t^{56}+\frac{454172380100815225}{4294967296}\cdot t^{54}-\frac{1487232668018916675}{34359738368}\cdot t^{52}+\frac{4382378928429074469}{274877906944}\cdot t^{50}-\frac{5803691013324990513}{1099511627776}\cdot t^{48}+\frac{862297611041963817}{549755813888}\cdot t^{46}-\frac{3672749084067623665}{8796093022208}\cdot t^{44}+\frac{3495392991476832985}{35184372088832}\cdot t^{42}-\frac{2965057503114830739}{140737488355328}\cdot t^{40}+\frac{558634022325982603}{140737488355328}\cdot t^{38}-\frac{745198705303919867}{1125899906842624}\cdot t^{36}+\frac{3503546151802011315}{36028797018963968}\cdot t^{34}-\frac{1804857108504066435}{144115188075855872}\cdot t^{32}+\frac{50634000329073357}{36028797018963968}\cdot t^{30}-\frac{629308289804197437}{4611686018427387904}\cdot t^{28}+\frac{209769429934732479}{18446744073709551616}\cdot t^{26}-\frac{59437719903041025}{73786976294838206464}\cdot t^{24}+\frac{3538570037368275}{73786976294838206464}\cdot t^{22}-\frac{1397281501935165}{590295810358705651712}\cdot t^{20}+\frac{449972009097765}{4722366482869645213696}\cdot t^{18}-\frac{57902201338905}{18889465931478580854784}\cdot t^{16}+\frac{725591495475}{9444732965739290427392}\cdot t^{14}-\frac{219364870725}{151115727451828646838272}\cdot t^{12}+\frac{11965356585}{604462909807314587353088}\cdot t^{10}-\frac{443161355}{2417851639229258349412352}\cdot t^8+\frac{2544815}{2417851639229258349412352}\cdot t^6-\frac{62475}{19342813113834066795298816}\cdot t^4+\frac{1225}{309485009821345068724781056}\cdot t^2-\frac{1}{1237940039285380274899124224}$
• $P_3$:
  $256\cdot t^{197}-12544\cdot t^{195}+302640\cdot t^{193}-4792576\cdot t^{191}+56031760\cdot t^{189}-515782512\cdot t^{187}+\frac{62291483793}{16}\cdot t^{185}-\frac{198242530695}{8}\cdot t^{183}+\frac{34750872249093}{256}\cdot t^{181}-\frac{166399679287985}{256}\cdot t^{179}+\frac{11280482088242081}{4096}\cdot t^{177}-\frac{10677247751972451}{1024}\cdot t^{175}+\frac{582656261733980525}{16384}\cdot t^{173}-\frac{1802236977563027495}{16384}\cdot t^{171}+\frac{162705058812910587825}{524288}\cdot t^{169}-\frac{210360748170134672565}{262144}\cdot t^{167}+\frac{32041871762486117543115}{16777216}\cdot t^{165}-\frac{70446299146317382248675}{16777216}\cdot t^{163}+\frac{2296549352169946661306805}{268435456}\cdot t^{161}-\frac{543581954865276995693025}{33554432}\cdot t^{159}+\frac{15343669516994931107640645}{536870912}\cdot t^{157}-\frac{25275568590949680702739755}{536870912}\cdot t^{155}+\frac{2493090174652763960224784925}{34359738368}\cdot t^{153}-\frac{1800599537320642194378496839}{17179869184}\cdot t^{151}+\frac{78129462682591083721595696175}{549755813888}\cdot t^{149}-\frac{99590226073786044984313774107}{549755813888}\cdot t^{147}+\frac{1911811656525577904698874973063}{8796093022208}\cdot t^{145}-\frac{540375614417561006201436395895}{2199023255552}\cdot t^{143}+\frac{9220896828876465371366695340373}{35184372088832}\cdot t^{141}-\frac{9284865507142492676534307591255}{35184372088832}\cdot t^{139}+\frac{282702047869852848446477917802307}{1125899906842624}\cdot t^{137}-\frac{127180426789431578912854369434339}{562949953421312}\cdot t^{135}+\frac{13859601931450706400804430982332485}{72057594037927936}\cdot t^{133}-\frac{11171679132623902735193874670607397}{72057594037927936}\cdot t^{131}+\frac{136480412932987850488057163300175015}{1152921504606846976}\cdot t^{129}-\frac{3086060169738025015417944621511407}{36028797018963968}\cdot t^{127}+\frac{33870462850581533811192009487946183}{576460752303423488}\cdot t^{125}-\frac{22032574038274877206373852067448625}{576460752303423488}\cdot t^{123}+\frac{1740109505359751617678136969074389825}{73786976294838206464}\cdot t^{121}-\frac{509320876024503980984650636811807375}{36893488147419103232}\cdot t^{119}+\frac{9053017393843145444286663597609366025}{1180591620717411303424}\cdot t^{117}-\frac{4771926055198041400103254557509488725}{1180591620717411303424}\cdot t^{115}+\frac{38192888024204104246247660103143710125}{18889465931478580854784}\cdot t^{113}-\frac{4532719343907793917296609023493874675}{4722366482869645213696}\cdot t^{111}+\frac{32670899167127605507787246857650655125}{75557863725914323419136}\cdot t^{109}-\frac{13965207879281996079799254539152632975}{75557863725914323419136}\cdot t^{107}+\frac{181228132456311669950896046891383481925}{2417851639229258349412352}\cdot t^{105}-\frac{34856474679845769970828956461425736625}{1208925819614629174706176}\cdot t^{103}+\frac{813782495525465909585620036852752864405}{77371252455336267181195264}\cdot t^{101}-\frac{281441008245692565635350033290398710125}{77371252455336267181195264}\cdot t^{99}+\frac{1475967925405248255023873525936999073315}{1237940039285380274899124224}\cdot t^{97}-\frac{57290471694401392852067119654217250945}{154742504910672534362390528}\cdot t^{95}+\frac{269548952703374308835068165707144389325}{2475880078570760549798248448}\cdot t^{93}-\frac{75024750791479199297099649505215595155}{2475880078570760549798248448}\cdot t^{91}+\frac{1264305985560112432599271871291596140575}{158456325028528675187087900672}\cdot t^{89}-\frac{157375150650139869232636638524408470645}{79228162514264337593543950336}\cdot t^{87}+\frac{1184588407610006540843649224788354303185}{2535301200456458802993406410752}\cdot t^{85}-\frac{263094476494197048078376740854449723925}{2535301200456458802993406410752}\cdot t^{83}+\frac{882079313802711876463759654312997448785}{40564819207303340847894502572032}\cdot t^{81}-\frac{43560800157309878059727186928028772925}{10141204801825835211973625643008}\cdot t^{79}+\frac{129672294961035492079245857898798695055}{162259276829213363391578010288128}\cdot t^{77}-\frac{22700797837500888466188427678107274245}{162259276829213363391578010288128}\cdot t^{75}+\frac{119534561668054962986096559405593332125}{5192296858534827628530496329220096}\cdot t^{73}-\frac{9233886774357684971412750091649008725}{2596148429267413814265248164610048}\cdot t^{71}+\frac{342480725884758912745681850414146069875}{664613997892457936451903530140172288}\cdot t^{69}-\frac{46469623072622580063699804573255447075}{664613997892457936451903530140172288}\cdot t^{67}+\frac{94347416541385238311148088072973180425}{10633823966279326983230456482242756608}\cdot t^{65}-\frac{698710501901565511020237635267546625}{664613997892457936451903530140172288}\cdot t^{63}+\frac{1234915484356341577395949413282822225}{10633823966279326983230456482242756608}\cdot t^{61}-\frac{126946148543540337413469690276798375}{10633823966279326983230456482242756608}\cdot t^{59}+\frac{6205853147371357637555618287531486275}{5444517870735015415413993718908291383296}\cdot t^{57}-\frac{274607453232912465053198591186099925}{2722258935367507707706996859454145691648}\cdot t^{55}+\frac{719209996562389789425043929296928375}{87112285931760246646623899502532662132736}\cdot t^{53}-\frac{54305280836327294785080029291570811}{87112285931760246646623899502532662132736}\cdot t^{51}+\frac{60365503981096164647756789317134075}{1393796574908163946345982392040522594123776}\cdot t^{49}-\frac{961921852056491729346368350094169}{348449143727040986586495598010130648530944}\cdot t^{47}+\frac{897185092384009973618139936541671}{5575186299632655785383929568162090376495104}\cdot t^{45}-\frac{47666268190413753025757139485685}{5575186299632655785383929568162090376495104}\cdot t^{43}+\frac{73577162693920716208989225565083}{178405961588244985132285746181186892047843328}\cdot t^{41}-\frac{1604437650489708203685011301015}{89202980794122492566142873090593446023921664}\cdot t^{39}+\frac{4030129827162283996374892793397}{5708990770823839524233143877797980545530986496}\cdot t^{37}-\frac{141609500099719380689336214013}{5708990770823839524233143877797980545530986496}\cdot t^{35}+\frac{70864299881693045845378509115}{91343852333181432387730302044767688728495783936}\cdot t^{33}-\frac{244999674813606130214509251}{11417981541647679048466287755595961091061972992}\cdot t^{31}+\frac{95175312270949749832704095}{182687704666362864775460604089535377456991567872}\cdot t^{29}-\frac{2011513627381863531081617}{182687704666362864775460604089535377456991567872}\cdot t^{27}+\frac{2345652103691143187407467}{11692013098647223345629478661730264157247460343808}\cdot t^{25}-\frac{18217242184615899249825}{5846006549323611672814739330865132078623730171904}\cdot t^{23}+\frac{7618119459021194231745}{187072209578355573530071658587684226515959365500928}\cdot t^{21}-\frac{82455679125577300725}{187072209578355573530071658587684226515959365500928}\cdot t^{19}+\frac{11604873358414583065}{2993155353253689176481146537402947624255349848014848}\cdot t^{17}-\frac{20261153034101665}{748288838313422294120286634350736906063837462003712}\cdot t^{15}+\frac{1745218267908675}{11972621413014756705924586149611790497021399392059392}\cdot t^{13}-\frac{6970149764305}{11972621413014756705924586149611790497021399392059392}\cdot t^{11}+\frac{627427556525}{383123885216472214589586756787577295904684780545900544}\cdot t^9-\frac{577092285}{191561942608236107294793378393788647952342390272950272}\cdot t^7+\frac{79208745}{24519928653854221733733552434404946937899825954937634816}\cdot t^5-\frac{40425}{24519928653854221733733552434404946937899825954937634816}\cdot t^3+\frac{99}{392318858461667547739736838950479151006397215279002157056}\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.