Rule: Q[2, 42, 45, 90]

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.

• $P_1$:
  $4\cdot t^2-1$
• $P_2$:
  $4\cdot t^{44}-43\cdot t^{42}+\frac{861}{4}\cdot t^{40}-\frac{2665}{4}\cdot t^{38}+\frac{45695}{32}\cdot t^{36}-\frac{575757}{256}\cdot t^{34}+\frac{2760681}{1024}\cdot t^{32}-\frac{643467}{256}\cdot t^{30}+\frac{7565085}{4096}\cdot t^{28}-\frac{17651865}{16384}\cdot t^{26}+\frac{32782035}{65536}\cdot t^{24}-\frac{12096045}{65536}\cdot t^{22}+\frac{28224105}{524288}\cdot t^{20}-\frac{206253075}{16777216}\cdot t^{18}+\frac{145422675}{67108864}\cdot t^{16}-\frac{9694845}{33554432}\cdot t^{14}+\frac{30421755}{1073741824}\cdot t^{12}-\frac{8436285}{4294967296}\cdot t^{10}+\frac{1562275}{17179869184}\cdot t^8-\frac{44275}{17179869184}\cdot t^6+\frac{5313}{137438953472}\cdot t^4-\frac{253}{1099511627776}\cdot t^2+\frac{1}{4398046511104}$
• $P_3$:
  $4\cdot t^{89}-88\cdot t^{87}+\frac{3741}{4}\cdot t^{85}-\frac{25585}{4}\cdot t^{83}+\frac{2024785}{64}\cdot t^{81}-\frac{1929501}{16}\cdot t^{79}+\frac{94361787}{256}\cdot t^{77}-\frac{237609801}{256}\cdot t^{75}+\frac{16082126775}{8192}\cdot t^{73}-\frac{14493768575}{4096}\cdot t^{71}+\frac{1440680596355}{262144}\cdot t^{69}-\frac{1944670126035}{262144}\cdot t^{67}+\frac{36749279048405}{4194304}\cdot t^{65}-\frac{2386316821325}{262144}\cdot t^{63}+\frac{35041178586825}{4194304}\cdot t^{61}-\frac{28500158583951}{4194304}\cdot t^{59}+\frac{1317939765868653}{268435456}\cdot t^{57}-\frac{423737281693467}{134217728}\cdot t^{55}+\frac{7768516831046895}{4294967296}\cdot t^{53}-\frac{3967759893692595}{4294967296}\cdot t^{51}+\frac{28907964939760335}{68719476736}\cdot t^{49}-\frac{2932692095338005}{17179869184}\cdot t^{47}+\frac{16953155909413815}{274877906944}\cdot t^{45}-\frac{5445692521193925}{274877906944}\cdot t^{43}+\frac{49671316632708225}{8796093022208}\cdot t^{41}-\frac{6266227636741653}{4398046511104}\cdot t^{39}+\frac{357174975294274221}{1125899906842624}\cdot t^{37}-\frac{69923143311577493}{1125899906842624}\cdot t^{35}+\frac{191724747789809255}{18014398509481984}\cdot t^{33}-\frac{3576549845711535}{2251799813685248}\cdot t^{31}+\frac{7391536347803839}{36028797018963968}\cdot t^{29}-\frac{820383749920273}{36028797018963968}\cdot t^{27}+\frac{9929472283517787}{4611686018427387904}\cdot t^{25}-\frac{395911973027025}{2305843009213693952}\cdot t^{23}+\frac{841728816603675}{73786976294838206464}\cdot t^{21}-\frac{45912480905655}{73786976294838206464}\cdot t^{19}+\frac{32308782859535}{1180591620717411303424}\cdot t^{17}-\frac{280086337895}{295147905179352825856}\cdot t^{15}+\frac{119065042425}{4722366482869645213696}\cdot t^{13}-\frac{2334608675}{4722366482869645213696}\cdot t^{11}+\frac{1027227817}{151115727451828646838272}\cdot t^9-\frac{4601817}{75557863725914323419136}\cdot t^7+\frac{1533939}{4835703278458516698824704}\cdot t^5-\frac{3795}{4835703278458516698824704}\cdot t^3+\frac{45}{77371252455336267181195264}\cdot t$
• $P_4$:
  $4\cdot t^{179}-178\cdot t^{177}+3894\cdot t^{175}-55825\cdot t^{173}+\frac{37752925}{64}\cdot t^{171}-\frac{627130017}{128}\cdot t^{169}+\frac{8527526553}{256}\cdot t^{167}-\frac{97605322503}{512}\cdot t^{165}+\frac{15355814110065}{16384}\cdot t^{163}-\frac{131736721049505}{32768}\cdot t^{161}+\frac{249524848105533}{16384}\cdot t^{159}-\frac{1686004097393007}{32768}\cdot t^{157}+\frac{163863541084720347}{1048576}\cdot t^{155}-\frac{900834344931431295}{2097152}\cdot t^{153}+\frac{4507272703469312865}{4194304}\cdot t^{151}-\frac{20624187218905037655}{8388608}\cdot t^{149}+\frac{2773198637507889575415}{536870912}\cdot t^{147}-\frac{10739514463766569120815}{1073741824}\cdot t^{145}+\frac{19225056756125339784175}{1073741824}\cdot t^{143}-\frac{63809088344210714229725}{2147483648}\cdot t^{141}+\frac{12595914039147194988947715}{274877906944}\cdot t^{139}-\frac{36180716247217953620544335}{549755813888}\cdot t^{137}+\frac{96967650333452950497408235}{1099511627776}\cdot t^{135}-\frac{242889060444774837233192325}{2199023255552}\cdot t^{133}+\frac{9111453728992450945440009525}{70368744177664}\cdot t^{131}-\frac{20021684774805347045270111253}{140737488355328}\cdot t^{129}+\frac{2580217118831058710129714637}{17592186044416}\cdot t^{127}-\frac{4997413983966908917876506127}{35184372088832}\cdot t^{125}+\frac{145601347277231368847905723625}{1125899906842624}\cdot t^{123}-\frac{249474059972840137123963609125}{2251799813685248}\cdot t^{121}+\frac{402484816756182087893327956055}{4503599627370496}\cdot t^{119}-\frac{611787377883774505109126559745}{9007199254740992}\cdot t^{117}+\frac{56102556031341807995547741005805}{1152921504606846976}\cdot t^{115}-\frac{75809576331776036159722828755525}{2305843009213693952}\cdot t^{113}+\frac{48320205381494637068767733719275}{2305843009213693952}\cdot t^{111}-\frac{58127064798822612670901874749985}{4611686018427387904}\cdot t^{109}+\frac{2111950021023888260376101449249455}{295147905179352825856}\cdot t^{107}-\frac{2263630423214226105574158253391355}{590295810358705651712}\cdot t^{105}+\frac{2290478523118916704305949604061675}{1180591620717411303424}\cdot t^{103}-\frac{2188013035450749126699245912008725}{2361183241434822606848}\cdot t^{101}+\frac{31569902368646523113803405301840175}{75557863725914323419136}\cdot t^{99}-\frac{26872362939165517393412935448188575}{151115727451828646838272}\cdot t^{97}+\frac{5396727132710259186668850390215925}{75557863725914323419136}\cdot t^{95}-\frac{4090372881947259763788222202056375}{151115727451828646838272}\cdot t^{93}+\frac{46787741146979618367609664653468375}{4835703278458516698824704}\cdot t^{91}-\frac{31538403291667742751499848025671275}{9671406556917033397649408}\cdot t^{89}+\frac{20036402869917404382685497220721725}{19342813113834066795298816}\cdot t^{87}-\frac{11991070730500881426272027692004475}{38685626227668133590597632}\cdot t^{85}+\frac{216202638928728013594904741719474625}{2475880078570760549798248448}\cdot t^{83}-\frac{114618722585209757012534792969523625}{4951760157141521099596496896}\cdot t^{81}+\frac{28566512398159970209277902247788965}{4951760157141521099596496896}\cdot t^{79}-\frac{13377933530738846057878889926347135}{9903520314283042199192993792}\cdot t^{77}+\frac{1505532058113148598667447381711219885}{5070602400912917605986812821504}\cdot t^{75}-\frac{620688079225076119640791336242554625}{10141204801825835211973625643008}\cdot t^{73}+\frac{239736665520796596475014643098976125}{20282409603651670423947251286016}\cdot t^{71}-\frac{86653907464607933416787110996502643}{40564819207303340847894502572032}\cdot t^{69}+\frac{468410292423894497225305443312892167}{1298074214633706907132624082305024}\cdot t^{67}-\frac{147718607409674901350042837707146567}{2596148429267413814265248164610048}\cdot t^{65}+\frac{5427761154114679812183597767645295}{649037107316853453566312041152512}\cdot t^{63}-\frac{1484860279308862540018849480348965}{1298074214633706907132624082305024}\cdot t^{61}+\frac{6038431802522707662743321220085791}{41538374868278621028243970633760768}\cdot t^{59}-\frac{1423303046441156193821989613936739}{83076749736557242056487941267521536}\cdot t^{57}+\frac{310496399961739377438476684505609}{166153499473114484112975882535043072}\cdot t^{55}-\frac{62554219772511596187238892482815}{332306998946228968225951765070086144}\cdot t^{53}+\frac{1486201980112430681827848169677915}{85070591730234615865843651857942052864}\cdot t^{51}-\frac{253499334400448042719800189476835}{170141183460469231731687303715884105728}\cdot t^{49}+\frac{19810952768137087868054560262145}{170141183460469231731687303715884105728}\cdot t^{47}-\frac{2828640858850375377805703294595}{340282366920938463463374607431768211456}\cdot t^{45}+\frac{11766195169167527832048933872475}{21778071482940061661655974875633165533184}\cdot t^{43}-\frac{1387240401848580445533383899575}{43556142965880123323311949751266331066368}\cdot t^{41}+\frac{147732094742316359134723999695}{87112285931760246646623899502532662132736}\cdot t^{39}-\frac{14145171495549350319011562705}{174224571863520493293247799005065324265472}\cdot t^{37}+\frac{19384123901308368955682511855}{5575186299632655785383929568162090376495104}\cdot t^{35}-\frac{1476578379372484896764958975}{11150372599265311570767859136324180752990208}\cdot t^{33}+\frac{24848080835946966646223175}{5575186299632655785383929568162090376495104}\cdot t^{31}-\frac{1467220011265439935300797}{11150372599265311570767859136324180752990208}\cdot t^{29}+\frac{1205852883752568043992153}{356811923176489970264571492362373784095686656}\cdot t^{27}-\frac{53367086394799064864613}{713623846352979940529142984724747568191373312}\cdot t^{25}+\frac{2012333574464519791275}{1427247692705959881058285969449495136382746624}\cdot t^{23}-\frac{63807544095691628925}{2854495385411919762116571938898990272765493248}\cdot t^{21}+\frac{53598337040380968297}{182687704666362864775460604089535377456991567872}\cdot t^{19}-\frac{1142949948111378673}{365375409332725729550921208179070754913983135744}\cdot t^{17}+\frac{9671552572371049}{365375409332725729550921208179070754913983135744}\cdot t^{15}-\frac{126135016780395}{730750818665451459101842416358141509827966271488}\cdot t^{13}+\frac{78083581816435}{93536104789177786765035829293842113257979682750464}\cdot t^{11}-\frac{531838637759}{187072209578355573530071658587684226515959365500928}\cdot t^9+\frac{2368405611}{374144419156711147060143317175368453031918731001856}\cdot t^7-\frac{6147141}{748288838313422294120286634350736906063837462003712}\cdot t^5+\frac{121485}{23945242826029513411849172299223580994042798784118784}\cdot t^3-\frac{45}{47890485652059026823698344598447161988085597568237568}\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.