Rule: Q[4, 20, 25, 50, 100]

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.

• $P_1$:
  $16\cdot t^4-12\cdot t^2+1$
• $P_2$:
  $16\cdot t^{24}-92\cdot t^{22}+231\cdot t^{20}-\frac{665}{2}\cdot t^{18}+\frac{4845}{16}\cdot t^{16}-\frac{2907}{16}\cdot t^{14}+\frac{4641}{64}\cdot t^{12}-\frac{2431}{128}\cdot t^{10}+\frac{6435}{2048}\cdot t^8-\frac{5005}{16384}\cdot t^6+\frac{1001}{65536}\cdot t^4-\frac{39}{131072}\cdot t^2+\frac{1}{1048576}$
• $P_3$:
  $16\cdot t^{49}-192\cdot t^{47}+1081\cdot t^{45}-3795\cdot t^{43}+\frac{148995}{16}\cdot t^{41}-\frac{135751}{8}\cdot t^{39}+\frac{3048227}{128}\cdot t^{37}-\frac{3372291}{128}\cdot t^{35}+\frac{95548245}{4096}\cdot t^{33}-\frac{8544965}{512}\cdot t^{31}+\frac{158936349}{16384}\cdot t^{29}-\frac{75207643}{16384}\cdot t^{27}+\frac{463120749}{262144}\cdot t^{25}-\frac{72212175}{131072}\cdot t^{23}+\frac{289994925}{2097152}\cdot t^{21}-\frac{57998985}{2097152}\cdot t^{19}+\frac{583401555}{134217728}\cdot t^{17}-\frac{17678835}{33554432}\cdot t^{15}+\frac{206253075}{4294967296}\cdot t^{13}-\frac{13656825}{4294967296}\cdot t^{11}+\frac{10015005}{68719476736}\cdot t^9-\frac{148005}{34359738368}\cdot t^7+\frac{40365}{549755813888}\cdot t^5-\frac{325}{549755813888}\cdot t^3+\frac{25}{17592186044416}\cdot t$
• $P_4$:
  $16\cdot t^{99}-392\cdot t^{97}+4656\cdot t^{95}-35720\cdot t^{93}+\frac{3183545}{16}\cdot t^{91}-\frac{27445509}{32}\cdot t^{89}+\frac{190561371}{64}\cdot t^{87}-\frac{1095069261}{128}\cdot t^{85}+\frac{84986896995}{4096}\cdot t^{83}-\frac{353126264315}{8192}\cdot t^{81}+\frac{635627275767}{8192}\cdot t^{79}-\frac{2000375522613}{16384}\cdot t^{77}+\frac{88683314835843}{524288}\cdot t^{75}-\frac{217591687594575}{1048576}\cdot t^{73}+\frac{474942653653275}{2097152}\cdot t^{71}-\frac{925672544571285}{4194304}\cdot t^{69}+\frac{51705423561053205}{268435456}\cdot t^{67}-\frac{81021042872777205}{536870912}\cdot t^{65}+\frac{14271999422033925}{134217728}\cdot t^{63}-\frac{18111250728545975}{268435456}\cdot t^{61}+\frac{662871776664782685}{17179869184}\cdot t^{59}-\frac{683648951099121865}{34359738368}\cdot t^{57}+\frac{635841332141141315}{68719476736}\cdot t^{55}-\frac{533158880987913525}{137438953472}\cdot t^{53}+\frac{6444674894748638925}{4398046511104}\cdot t^{51}-\frac{4382378928429074469}{8796093022208}\cdot t^{49}+\frac{1339313310767305503}{8796093022208}\cdot t^{47}-\frac{734549816813524733}{17592186044416}\cdot t^{45}+\frac{5771462846391980045}{562949953421312}\cdot t^{43}-\frac{2531146649000465265}{1125899906842624}\cdot t^{41}+\frac{988352501038276913}{2251799813685248}\cdot t^{39}-\frac{342388594328828047}{4503599627370496}\cdot t^{37}+\frac{6706788347735278803}{576460752303423488}\cdot t^{35}-\frac{1804857108504066435}{1152921504606846976}\cdot t^{33}+\frac{106168065206121555}{576460752303423488}\cdot t^{31}-\frac{21700285855317153}{1152921504606846976}\cdot t^{29}+\frac{489462003181042451}{295147905179352825856}\cdot t^{27}-\frac{73702772679770871}{590295810358705651712}\cdot t^{25}+\frac{9384903142585425}{1180591620717411303424}\cdot t^{23}-\frac{998058215667975}{2361183241434822606848}\cdot t^{21}+\frac{1397281501935165}{75557863725914323419136}\cdot t^{19}-\frac{98774343460485}{151115727451828646838272}\cdot t^{17}+\frac{2757247682805}{151115727451828646838272}\cdot t^{15}-\frac{118119545775}{302231454903657293676544}\cdot t^{13}+\frac{59826782925}{9671406556917033397649408}\cdot t^{11}-\frac{1329484065}{19342813113834066795298816}\cdot t^9+\frac{19267885}{38685626227668133590597632}\cdot t^7-\frac{162435}{77371252455336267181195264}\cdot t^5+\frac{20825}{4951760157141521099596496896}\cdot t^3-\frac{25}{9903520314283042199192993792}\cdot t$
• $P_5$:
  $16\cdot t^{199}-792\cdot t^{197}+19306\cdot t^{195}-308945\cdot t^{193}+3650595\cdot t^{191}-\frac{67938509}{2}\cdot t^{189}+\frac{2073875517}{8}\cdot t^{187}-\frac{26696350197}{16}\cdot t^{185}+\frac{37864323362745}{4096}\cdot t^{183}-\frac{366814762629315}{8192}\cdot t^{181}+\frac{6289907877085833}{32768}\cdot t^{179}-\frac{48198423467943437}{65536}\cdot t^{177}+\frac{665548443206282779}{262144}\cdot t^{175}-\frac{4168233257020014525}{524288}\cdot t^{173}+\frac{47630548692737155225}{2097152}\cdot t^{171}-\frac{249481090179796234665}{4194304}\cdot t^{169}+\frac{38496016915134645079395}{268435456}\cdot t^{167}-\frac{171518254728602158613145}{536870912}\cdot t^{165}+\frac{1416753349498160687445575}{2147483648}\cdot t^{163}-\frac{5439195834086715776779275}{4294967296}\cdot t^{161}+\frac{19460233984176916445810295}{8589934592}\cdot t^{159}-\frac{65027932714883279456191305}{17179869184}\cdot t^{157}+\frac{406706876418008498580448785}{68719476736}\cdot t^{155}-\frac{1192347474833930589672723225}{137438953472}\cdot t^{153}+\frac{105034973010370794672078982275}{8796093022208}\cdot t^{151}-\frac{271890530135416971351153022689}{17592186044416}\cdot t^{149}+\frac{1325316085443460444791252532347}{70368744177664}\cdot t^{147}-\frac{3044737082614809255631541623767}{140737488355328}\cdot t^{145}+\frac{13200604295057561722920803385435}{562949953421312}\cdot t^{143}-\frac{27026766567396536433316175997645}{1125899906842624}\cdot t^{141}+\frac{104609484713805417488953198861473}{4503599627370496}\cdot t^{139}-\frac{191507838879577736044388266898337}{9007199254740992}\cdot t^{137}+\frac{21239131273835073678446679695534613}{1152921504606846976}\cdot t^{135}-\frac{34858998797285110038386902167684735}{2305843009213693952}\cdot t^{133}+\frac{108431003346055526547469960038248265}{9223372036854775808}\cdot t^{131}-\frac{159877055150071482000295534151633589}{18446744073709551616}\cdot t^{129}+\frac{55891978629699786390347219256262149}{9223372036854775808}\cdot t^{127}-\frac{74148851105327141586663588338476779}{18446744073709551616}\cdot t^{125}+\frac{186697074745381854222431062255748875}{73786976294838206464}\cdot t^{123}-\frac{223090962225609181753607303727485875}{147573952589676412928}\cdot t^{121}+\frac{16196403857579226595311890250615474525}{18889465931478580854784}\cdot t^{119}-\frac{17443618880819719270698693273442436975}{37778931862957161709568}\cdot t^{117}+\frac{35675828126956785705533855501380463325}{151115727451828646838272}\cdot t^{115}-\frac{34640061231254885246596714977269876625}{302231454903657293676544}\cdot t^{113}+\frac{63870136209609823380088581694686415875}{1208925819614629174706176}\cdot t^{111}-\frac{55903538574862791646658177956424454325}{2417851639229258349412352}\cdot t^{109}+\frac{92898991544788930443881997586537080225}{9671406556917033397649408}\cdot t^{107}-\frac{73262436524891951682277125339069918225}{19342813113834066795298816}\cdot t^{105}+\frac{1754442558885570421865057475225095410125}{1237940039285380274899124224}\cdot t^{103}-\frac{1245585452334896800386153117631764588375}{2475880078570760549798248448}\cdot t^{101}+\frac{1677388409144327691186686198410776312345}{9903520314283042199192993792}\cdot t^{99}-\frac{1070800259607729126193790597248411092405}{19807040628566084398385987584}\cdot t^{97}+\frac{647823026082846519173374353013071991455}{39614081257132168796771975168}\cdot t^{95}-\frac{371265538629175934810565586728708309825}{79228162514264337593543950336}\cdot t^{93}+\frac{402910698694980885114053673268750418425}{316912650057057350374175801344}\cdot t^{91}-\frac{206886434000745670788971760756806641185}{633825300114114700748351602688}\cdot t^{89}+\frac{3214949506138571614323862758427201614605}{40564819207303340847894502572032}\cdot t^{87}-\frac{1475539946321236217542089385262686939055}{81129638414606681695789005144064}\cdot t^{85}+\frac{1279183489161440819967280015878531416325}{324518553658426726783156020576256}\cdot t^{83}-\frac{523267389543981621631043862728049334025}{649037107316853453566312041152512}\cdot t^{81}+\frac{403663414791071536686805265533066629105}{2596148429267413814265248164610048}\cdot t^{79}-\frac{146678497578876212351933839262575573095}{5192296858534827628530496329220096}\cdot t^{77}+\frac{100322880765729732898961761029054728115}{20769187434139310514121985316880384}\cdot t^{75}-\frac{32255357910427529694660976347541057875}{41538374868278621028243970633760768}\cdot t^{73}+\frac{1246574714538287471140721262372616177875}{10633823966279326983230456482242756608}\cdot t^{71}-\frac{353018594373520725445548984273042872025}{21267647932558653966460912964485513216}\cdot t^{69}+\frac{187286662686630398438547697219484074575}{85070591730234615865843651857942052864}\cdot t^{67}-\frac{46469623072622580063699804573255447075}{170141183460469231731687303715884105728}\cdot t^{65}+\frac{5384180926417945996685360601179329875}{170141183460469231731687303715884105728}\cdot t^{63}-\frac{1163326180915394239575894374831644125}{340282366920938463463374607431768211456}\cdot t^{61}+\frac{467887233203334386466788287020199725}{1361129467683753853853498429727072845824}\cdot t^{59}-\frac{87406382357343065317684764613119525}{2722258935367507707706996859454145691648}\cdot t^{57}+\frac{3875016284508875895750691231181632275}{1393796574908163946345982392040522594123776}\cdot t^{55}-\frac{620688079225076119640791336242554625}{2787593149816327892691964784081045188247552}\cdot t^{53}+\frac{183463786609213833733378477336387875}{11150372599265311570767859136324180752990208}\cdot t^{51}-\frac{24951074978853081387739472917748751}{22300745198530623141535718272648361505980416}\cdot t^{49}+\frac{6227178305418341195242279319030673}{89202980794122492566142873090593446023921664}\cdot t^{47}-\frac{710757021239280628450734235442103}{178405961588244985132285746181186892047843328}\cdot t^{45}+\frac{147887652590770874772220868660715}{713623846352979940529142984724747568191373312}\cdot t^{43}-\frac{13970347346946971432086561816155}{1427247692705959881058285969449495136382746624}\cdot t^{41}+\frac{38185616081655055247703268964157}{91343852333181432387730302044767688728495783936}\cdot t^{39}-\frac{2935526664229317972668131787783}{182687704666362864775460604089535377456991567872}\cdot t^{37}+\frac{404105158821150427820788708281}{730750818665451459101842416358141509827966271488}\cdot t^{35}-\frac{24759815621314437705011768245}{1461501637330902918203684832716283019655932542976}\cdot t^{33}+\frac{1341664885884033570222312565}{2923003274661805836407369665432566039311865085952}\cdot t^{31}-\frac{63823444699342773417225099}{5846006549323611672814739330865132078623730171904}\cdot t^{29}+\frac{5286070695212804163074947}{23384026197294446691258957323460528314494920687616}\cdot t^{27}-\frac{188730629032620716228187}{46768052394588893382517914646921056628989841375232}\cdot t^{25}+\frac{183828534772033165157325}{2993155353253689176481146537402947624255349848014848}\cdot t^{23}-\frac{4707826631979389693775}{5986310706507378352962293074805895248510699696029696}\cdot t^{21}+\frac{199725978326398350645}{23945242826029513411849172299223580994042798784118784}\cdot t^{19}-\frac{3443204183265865305}{47890485652059026823698344598447161988085597568237568}\cdot t^{17}+\frac{94258407593429485}{191561942608236107294793378393788647952342390272950272}\cdot t^{15}-\frac{994586754829675}{383123885216472214589586756787577295904684780545900544}\cdot t^{13}+\frac{15571611175575}{1532495540865888858358347027150309183618739122183602176}\cdot t^{11}-\frac{85858507735}{3064991081731777716716694054300618367237478244367204352}\cdot t^9+\frac{19813501785}{392318858461667547739736838950479151006397215279002157056}\cdot t^7-\frac{41645835}{784637716923335095479473677900958302012794430558004314112}\cdot t^5+\frac{83325}{3138550867693340381917894711603833208051177722232017256448}\cdot t^3-\frac{25}{6277101735386680763835789423207666416102355444464034512896}\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.