Rule: Q[1, 50]

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.

• $P_1$:
  $-t+1$
• $P_2$:
  $-t^{51}+\frac{18131144153175521763929004298347530161083620289892271391693597284251}{7086160198304780325462239212620335436367989676318342355555206751}\cdot t^{50}-\frac{22288982038200387376663405505836959815217624289600667895735127261438750}{7086160198304780325462239212620335436367989676318342355555206751}\cdot t^{49}+\frac{357929220120545751624120742099411946508318479208321277013603212653541250}{144615514251117965825759983931027253803428360741190660317453199}\cdot t^{48}-\frac{202639718563479461431337775899608444436015478731423027556594823701263760000}{144615514251117965825759983931027253803428360741190660317453199}\cdot t^{47}+\frac{87967772759918354993829009521810387474455217037285255202671884196643972368000}{144615514251117965825759983931027253803428360741190660317453199}\cdot t^{46}-\frac{30473686098094663331691994350313947506836455238049143402342968482809884423648000}{144615514251117965825759983931027253803428360741190660317453199}\cdot t^{45}+\frac{8656606254398241896358512852681514169686492923845966539500128036620962721309600000}{144615514251117965825759983931027253803428360741190660317453199}\cdot t^{44}-\frac{2056421731075707682738139959073374290167519019512021701644037440438691119712603200000}{144615514251117965825759983931027253803428360741190660317453199}\cdot t^{43}+\frac{414575537793048720922761569402019239744434064826354195205333573747993002593939515200000}{144615514251117965825759983931027253803428360741190660317453199}\cdot t^{42}-\frac{71736703630511512036046994312229674156449381796014288792181110361817589660309235953280000}{144615514251117965825759983931027253803428360741190660317453199}\cdot t^{41}+\frac{10749579700442494102537907556495131143940852677249541052889786995150578924325719739626880000}{144615514251117965825759983931027253803428360741190660317453199}\cdot t^{40}-\frac{1404864904325394163918048106715573368602513310307756166108107483334513552923466771325184000000}{144615514251117965825759983931027253803428360741190660317453199}\cdot t^{39}+\frac{161044944285239326357231899090120122407510812846922102444216473975927140164609996551913728000000}{144615514251117965825759983931027253803428360741190660317453199}\cdot t^{38}-\frac{16267763088557462951004238074206016002445272053716874507661759553434156075434271854291404288000000}{144615514251117965825759983931027253803428360741190660317453199}\cdot t^{37}+\frac{1453411672521568099424617025670230014791229157800081582477502141207438888709997817023805632204800000}{144615514251117965825759983931027253803428360741190660317453199}\cdot t^{36}-\frac{115191625540024131495194027771201868496502205379305849876015023200887757767764248247821877077708800000}{144615514251117965825759983931027253803428360741190660317453199}\cdot t^{35}+\frac{8117924080418031029283396686312706152868864117446249245582744522403934282280757341939793234403840000000}{144615514251117965825759983931027253803428360741190660317453199}\cdot t^{34}-\frac{509621003691248754786308368078547832204121118413308386728625216842441435476574949751179977631585280000000}{144615514251117965825759983931027253803428360741190660317453199}\cdot t^{33}+\frac{28537009037013870199924075169881007137959640908327888766177880835523741612306770188288670108097735680000000}{144615514251117965825759983931027253803428360741190660317453199}\cdot t^{32}-\frac{1426672021252735120531739064907290090367133525057662490859214445429176476385460943160412883447693705216000000}{144615514251117965825759983931027253803428360741190660317453199}\cdot t^{31}+\frac{2055224979720055366268968091172231003494892214470335684933036340688840897564060611099705789437346840576000000}{4665016588745740833089031739710556574304140669070666461853329}\cdot t^{30}-\frac{81998603550793902558726134059300732491047403372012782241334828247974377135859590444574370979526095667200000000}{4665016588745740833089031739710556574304140669070666461853329}\cdot t^{29}+\frac{100768470672173072342518734940854753888062845662080135895634372238016912646116315133546593410198706585600000000}{160862640991232442520311439300364019803591057554160912477701}\cdot t^{28}-\frac{3206148326069564334031518610388993460693196925527491673734002437220826991138831776500691025642936310169600000000}{160862640991232442520311439300364019803591057554160912477701}\cdot t^{27}+\frac{90994555952891810170128519202625494264014100432892260163421544519673239813032112061909157596677165663911936000000}{160862640991232442520311439300364019803591057554160912477701}\cdot t^{26}-\frac{2300943494657473233357346848884006419569579041452474441139749027219666278675853127547512287025764021605236736000000}{160862640991232442520311439300364019803591057554160912477701}\cdot t^{25}+\frac{51759919781012949127114634224531249728583135917818289769225414280736766717890540312161723993933373517332480000000000}{160862640991232442520311439300364019803591057554160912477701}\cdot t^{24}-\frac{1033863606867640748202551213388330265228573286593821807105393698398090650357090264487266983833371166805852160000000000}{160862640991232442520311439300364019803591057554160912477701}\cdot t^{23}+\frac{18295222774499039253601034037763948103242683738118809172226751586634755739126013300361910321714670937476956160000000000}{160862640991232442520311439300364019803591057554160912477701}\cdot t^{22}-\frac{286065737100889383126781408088523015363408767689810863078980217904548649832089060240801904687831290221321781248000000000}{160862640991232442520311439300364019803591057554160912477701}\cdot t^{21}+\frac{3940100939579957143106469837490140696308886672336950894745214838813643516747380377515237431539730877072411721728000000000}{160862640991232442520311439300364019803591057554160912477701}\cdot t^{20}-\frac{47633575884058518110359084256995997337051494811969501958214937060701590105800930580544790640374885238260734361600000000000}{160862640991232442520311439300364019803591057554160912477701}\cdot t^{19}+\frac{503385948437445256588221627026571217735070549858226954584648563566060051123203573503509997955382774522272494387200000000000}{160862640991232442520311439300364019803591057554160912477701}\cdot t^{18}-\frac{4628334716295284184155518129501710416680799999091911203028050788706530613265316552028713818018803184827403285299200000000000}{160862640991232442520311439300364019803591057554160912477701}\cdot t^{17}+\frac{36824358972055714908512203372023185348546231576159075497831177480327008962115723589826572927021259422740018553159680000000000}{160862640991232442520311439300364019803591057554160912477701}\cdot t^{16}-\frac{251960156451466750857124469153651538077965208501551328949450310234758761674041735670158590269776058753357561756385280000000000}{160862640991232442520311439300364019803591057554160912477701}\cdot t^{15}+\frac{1471975568861375514380715830375840421011091170374150735965479882084276443619827656968887809139600307098023597441024000000000000}{160862640991232442520311439300364019803591057554160912477701}\cdot t^{14}-\frac{7281714616824826989885286852130267878454196756890660503394424984635479479684736695322016324938576574058795009835008000000000000}{160862640991232442520311439300364019803591057554160912477701}\cdot t^{13}+\frac{30208248175124072415478942755325116413828825383286285106260080221658924101624552500187947292558000637581801258221568000000000000}{160862640991232442520311439300364019803591057554160912477701}\cdot t^{12}-\frac{103904638838426020349237912945108659275682073352166948912119547835630773648614885554329765837375810035271766905769164800000000000}{160862640991232442520311439300364019803591057554160912477701}\cdot t^{11}+\frac{292346577897928072691047499231626215484176229616216971815757064187024875226759688660144719317236120751344755197922508800000000000}{160862640991232442520311439300364019803591057554160912477701}\cdot t^{10}-\frac{662018472019776625923815764845249819822585363119488436151313238979367953374674408714167556195754290786433573207408640000000000000}{160862640991232442520311439300364019803591057554160912477701}\cdot t^9+\frac{1182927133249912942407617785288431577326159108955504899150555403156543779304834550799570224743244527367110473421946880000000000000}{160862640991232442520311439300364019803591057554160912477701}\cdot t^8-\frac{1627339948444502540286716366421644997697091550359234097207319824579584297568444626229698681642720737416334250638049280000000000000}{160862640991232442520311439300364019803591057554160912477701}\cdot t^7+\frac{1670419377687357558750521008760410001805567575487148516879707747115275858189480846967176005277069182785845880858607616000000000000}{160862640991232442520311439300364019803591057554160912477701}\cdot t^6-\frac{1227792809010114014147787631891761656962497318717232969669826536277829507064338948552880088251181048996969582539309056000000000000}{160862640991232442520311439300364019803591057554160912477701}\cdot t^5+\frac{610798344497983547485866163490602594536879285435338651733979676704560404198634051526903699458073149022094702621491200000000000000}{160862640991232442520311439300364019803591057554160912477701}\cdot t^4-\frac{189505135869202858936005167168954627392937729524758929228712242576474754028816504466006705977158509100373492786790400000000000000}{160862640991232442520311439300364019803591057554160912477701}\cdot t^3+\frac{32218314533708179967152949358558683866576352553870301447242476250262537957608059710355298147237422790621199230566400000000000000}{160862640991232442520311439300364019803591057554160912477701}\cdot t^2-\frac{2370365063641756581807253114478627546755988546214627230647106105040744381365291937013483860628311594412271166554112000000000000}{160862640991232442520311439300364019803591057554160912477701}\cdot t+\frac{42416960089938407181220985887697262435017037021953536186564982550205602472979197984285173911326065991663654797312000000000000}{160862640991232442520311439300364019803591057554160912477701}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Laguerre type can be downloaded here packed into a single file.