Rule: Q[1, 2, 12, 32, 48, 96]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^3-1\cdot t$
• $P_3$:
  $2\cdot t^{15}-7\cdot t^{13}+\frac{39}{4}\cdot t^{11}-\frac{55}{8}\cdot t^9+\frac{165}{64}\cdot t^7-\frac{63}{128}\cdot t^5+\frac{21}{512}\cdot t^3-\frac{1}{1024}\cdot t$
• $P_4$:
  $2\cdot t^{47}-23\cdot t^{45}+\frac{495}{4}\cdot t^{43}-\frac{3311}{8}\cdot t^{41}+\frac{61705}{64}\cdot t^{39}-\frac{212667}{128}\cdot t^{37}+\frac{1124097}{512}\cdot t^{35}-\frac{2330445}{1024}\cdot t^{33}+\frac{15380937}{8192}\cdot t^{31}-\frac{20376455}{16384}\cdot t^{29}+\frac{43541267}{65536}\cdot t^{27}-\frac{37550331}{131072}\cdot t^{25}+\frac{104306475}{1048576}\cdot t^{23}-\frac{57998985}{2097152}\cdot t^{21}+\frac{51175575}{8388608}\cdot t^{19}-\frac{17678835}{16777216}\cdot t^{17}+\frac{300540195}{2147483648}\cdot t^{15}-\frac{59879925}{4294967296}\cdot t^{13}+\frac{17298645}{17179869184}\cdot t^{11}-\frac{1726725}{34359738368}\cdot t^9+\frac{444015}{274877906944}\cdot t^7-\frac{16445}{549755813888}\cdot t^5+\frac{575}{2199023255552}\cdot t^3-\frac{3}{4398046511104}\cdot t$
• $P_5$:
  $2\cdot t^{95}-47\cdot t^{93}+\frac{2139}{4}\cdot t^{91}-\frac{31395}{8}\cdot t^{89}+\frac{1336335}{64}\cdot t^{87}-\frac{10987317}{128}\cdot t^{85}+\frac{145276747}{512}\cdot t^{83}-\frac{793542167}{1024}\cdot t^{81}+\frac{29216779785}{16384}\cdot t^{79}-\frac{114964110495}{32768}\cdot t^{77}+\frac{782290668159}{131072}\cdot t^{75}-\frac{2321771769135}{262144}\cdot t^{73}+\frac{24212762735265}{2097152}\cdot t^{71}-\frac{55763406299475}{4194304}\cdot t^{69}+\frac{227911064771025}{16777216}\cdot t^{67}-\frac{414741863546285}{33554432}\cdot t^{65}+\frac{5391644226101705}{536870912}\cdot t^{63}-\frac{7840566771092055}{1073741824}\cdot t^{61}+\frac{20439084317804075}{4294967296}\cdot t^{59}-\frac{23903809478990275}{8589934592}\cdot t^{57}+\frac{100395999811759155}{68719476736}\cdot t^{55}-\frac{94659085536801489}{137438953472}\cdot t^{53}+\frac{160245970355912103}{549755813888}\cdot t^{51}-\frac{121687678501362675}{1099511627776}\cdot t^{49}+\frac{662521805174085675}{17592186044416}\cdot t^{47}-\frac{403485110644048797}{35184372088832}\cdot t^{45}+\frac{438956329162206933}{140737488355328}\cdot t^{43}-\frac{212763051655111573}{281474976710656}\cdot t^{41}+\frac{366524584784015735}{2251799813685248}\cdot t^{39}-\frac{139781120599565445}{4503599627370496}\cdot t^{37}+\frac{94034572039707663}{18014398509481984}\cdot t^{35}-\frac{27767032438524099}{36028797018963968}\cdot t^{33}+\frac{916312070471295267}{9223372036854775808}\cdot t^{31}-\frac{204947144189106445}{18446744073709551616}\cdot t^{29}+\frac{78945484384039105}{73786976294838206464}\cdot t^{27}-\frac{12978859493582073}{147573952589676412928}\cdot t^{25}+\frac{7210477496434485}{1180591620717411303424}\cdot t^{23}-\frac{835662302610135}{2361183241434822606848}\cdot t^{21}+\frac{159245992330425}{9444732965739290427392}\cdot t^{19}-\frac{12249691717725}{18889465931478580854784}\cdot t^{17}+\frac{5949850262895}{302231454903657293676544}\cdot t^{15}-\frac{277044025545}{604462909807314587353088}\cdot t^{13}+\frac{19055938265}{2417851639229258349412352}\cdot t^{11}-\frac{459884425}{4835703278458516698824704}\cdot t^9+\frac{28943775}{38685626227668133590597632}\cdot t^7-\frac{264845}{77371252455336267181195264}\cdot t^5+\frac{2303}{309485009821345068724781056}\cdot t^3-\frac{3}{618970019642690137449562112}\cdot t$
• $P_6$:
  $2\cdot t^{191}-95\cdot t^{189}+\frac{8883}{4}\cdot t^{187}-\frac{272459}{8}\cdot t^{185}+\frac{24666235}{64}\cdot t^{183}-\frac{439322793}{128}\cdot t^{181}+\frac{12825391215}{512}\cdot t^{179}-\frac{157777071387}{1024}\cdot t^{177}+\frac{13356172086543}{16384}\cdot t^{175}-\frac{123465525208025}{32768}\cdot t^{173}+\frac{2018593498950545}{131072}\cdot t^{171}-\frac{14736442243719825}{262144}\cdot t^{169}+\frac{387404692762678955}{2097152}\cdot t^{167}-\frac{2307613427753972065}{4194304}\cdot t^{165}+\frac{25057792678580451075}{16777216}\cdot t^{163}-\frac{124609430032127192295}{33554432}\cdot t^{161}+\frac{9119144652351126345225}{1073741824}\cdot t^{159}-\frac{38502714614515125385671}{2147483648}\cdot t^{157}+\frac{301088277885920961349251}{8589934592}\cdot t^{155}-\frac{1093242651830990773867755}{17179869184}\cdot t^{153}+\frac{14781657622663675254109599}{137438953472}\cdot t^{151}-\frac{46617174206813178015257925}{274877906944}\cdot t^{149}+\frac{274866825029049251762691915}{1099511627776}\cdot t^{147}-\frac{758836094516780941771403895}{2199023255552}\cdot t^{145}+\frac{15718747672133319508121937825}{35184372088832}\cdot t^{143}-\frac{38225735356926848614601684967}{70368744177664}\cdot t^{141}+\frac{174832255779827616230824203255}{281474976710656}\cdot t^{139}-\frac{376389711601420127333296281351}{562949953421312}\cdot t^{137}+\frac{3054395952333475528081000136817}{4503599627370496}\cdot t^{135}-\frac{5844512669527456346835761844195}{9007199254740992}\cdot t^{133}+\frac{21112400087700416383754863155697}{36028797018963968}\cdot t^{131}-\frac{36019252002959135545516461585005}{72057594037927936}\cdot t^{129}+\frac{929296701676345697074324708893129}{2305843009213693952}\cdot t^{127}-\frac{1417057920738029716464965122137207}{4611686018427387904}\cdot t^{125}+\frac{4088681640253064148400401971914875}{18446744073709551616}\cdot t^{123}-\frac{5582780408884211156587482437721075}{36893488147419103232}\cdot t^{121}+\frac{28868223481837160254148947648044875}{295147905179352825856}\cdot t^{119}-\frac{35341551362855920164669531200858425}{590295810358705651712}\cdot t^{117}+\frac{81964377152542814161807053564260175}{2361183241434822606848}\cdot t^{115}-\frac{90041309239972875285846361004478875}{4722366482869645213696}\cdot t^{113}+\frac{749712374829668887906362858468871475}{75557863725914323419136}\cdot t^{111}-\frac{739298021052354799009585729438291125}{151115727451828646838272}\cdot t^{109}+\frac{1381431159337828681577911620150406845}{604462909807314587353088}\cdot t^{107}-\frac{1222740144311663251635451349753856285}{1208925819614629174706176}\cdot t^{105}+\frac{4100836110529288300939535853597085575}{9671406556917033397649408}\cdot t^{103}-\frac{3256491623372691072537472689182991765}{19342813113834066795298816}\cdot t^{101}+\frac{4897344460402647384250815092428263375}{77371252455336267181195264}\cdot t^{99}-\frac{3485989431755428094057330009298533475}{154742504910672534362390528}\cdot t^{97}+\frac{37571219431141836124840112322439749675}{4951760157141521099596496896}\cdot t^{95}-\frac{23941129550456443313459554947865489125}{9903520314283042199192993792}\cdot t^{93}+\frac{28850747103338778730980274948441848585}{39614081257132168796771975168}\cdot t^{91}-\frac{16429399163978904033286639676521953825}{79228162514264337593543950336}\cdot t^{89}+\frac{35350289629748015491401363172120863285}{633825300114114700748351602688}\cdot t^{87}-\frac{17951056536566760683226890135320232055}{1267650600228229401496703205376}\cdot t^{85}+\frac{17199482510881195823703703108720673225}{5070602400912917605986812821504}\cdot t^{83}-\frac{7767729128670034424427830348901984205}{10141204801825835211973625643008}\cdot t^{81}+\frac{26436389051355999511708162111809273975}{162259276829213363391578010288128}\cdot t^{79}-\frac{10584862204967879726520188104806286305}{324518553658426726783156020576256}\cdot t^{77}+\frac{7969970872809062295367491094869581505}{1298074214633706907132624082305024}\cdot t^{75}-\frac{2818487214482623661226556363994276625}{2596148429267413814265248164610048}\cdot t^{73}+\frac{3740901211949664132173429355846948975}{20769187434139310514121985316880384}\cdot t^{71}-\frac{1163326180915394239575894374831644125}{41538374868278621028243970633760768}\cdot t^{69}+\frac{677211717227671187604230323413160575}{166153499473114484112975882535043072}\cdot t^{67}-\frac{184239584937908329739504521356773475}{332306998946228968225951765070086144}\cdot t^{65}+\frac{11975573020964041433067793888190275875}{170141183460469231731687303715884105728}\cdot t^{63}-\frac{2833227632942795023474427796927390525}{340282366920938463463374607431768211456}\cdot t^{61}+\frac{1246947226619844851601299391144089625}{1361129467683753853853498429727072845824}\cdot t^{59}-\frac{254749457283170691473411732328064161}{2722258935367507707706996859454145691648}\cdot t^{57}+\frac{192874826292191851798655182540602657}{21778071482940061661655974875633165533184}\cdot t^{55}-\frac{33747981270638022849181447634357835}{43556142965880123323311949751266331066368}\cdot t^{53}+\frac{10891034705137984891375183803312669}{174224571863520493293247799005065324265472}\cdot t^{51}-\frac{1616350744855189237167193498920225}{348449143727040986586495598010130648530944}\cdot t^{49}+\frac{1760026366620094947137610698824245}{5575186299632655785383929568162090376495104}\cdot t^{47}-\frac{219015598286672342334034438290435}{11150372599265311570767859136324180752990208}\cdot t^{45}+\frac{49662263468576641985958335755275}{44601490397061246283071436545296723011960832}\cdot t^{43}-\frac{5110544035569767260777250961483}{89202980794122492566142873090593446023921664}\cdot t^{41}+\frac{1901382082199278200470665058265}{713623846352979940529142984724747568191373312}\cdot t^{39}-\frac{159110572886466984364625952363}{1427247692705959881058285969449495136382746624}\cdot t^{37}+\frac{23834377314976835714539110273}{5708990770823839524233143877797980545530986496}\cdot t^{35}-\frac{1588602498309758849574411405}{11417981541647679048466287755595961091061972992}\cdot t^{33}+\frac{1497825212692058343884445039}{365375409332725729550921208179070754913983135744}\cdot t^{31}-\frac{77465101090179860961657985}{730750818665451459101842416358141509827966271488}\cdot t^{29}+\frac{6973576727852111651980741}{2923003274661805836407369665432566039311865085952}\cdot t^{27}-\frac{270556585771647086309853}{5846006549323611672814739330865132078623730171904}\cdot t^{25}+\frac{35787908170852789194425}{46768052394588893382517914646921056628989841375232}\cdot t^{23}-\frac{995529496121578412995}{93536104789177786765035829293842113257979682750464}\cdot t^{21}+\frac{45866870159177592525}{374144419156711147060143317175368453031918731001856}\cdot t^{19}-\frac{858591658152092865}{748288838313422294120286634350736906063837462003712}\cdot t^{17}+\frac{102070336983115935}{11972621413014756705924586149611790497021399392059392}\cdot t^{15}-\frac{1169126800832025}{23945242826029513411849172299223580994042798784118784}\cdot t^{13}+\frac{19867514262505}{95780971304118053647396689196894323976171195136475136}\cdot t^{11}-\frac{118889488025}{191561942608236107294793378393788647952342390272950272}\cdot t^9+\frac{1860878943}{1532495540865888858358347027150309183618739122183602176}\cdot t^7-\frac{4244429}{3064991081731777716716694054300618367237478244367204352}\cdot t^5+\frac{9215}{12259964326927110866866776217202473468949912977468817408}\cdot t^3-\frac{3}{24519928653854221733733552434404946937899825954937634816}\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.