Rule: Q[1, 3, 18]

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.

• $P_1$:
  $-t+1$
• $P_2$:
  $-t^4+\frac{49}{4}\cdot t^3-\frac{153}{4}\cdot t^2+\frac{57}{2}\cdot t-\frac{3}{2}$
• $P_3$:
  $-t^{22}+\frac{135595138927459374882635564209839292268037472324641394710211}{332039463404475229927595034298271053249034681825839655227}\cdot t^{21}-\frac{10022569269274085312736997941445429054325663734958826187136281323}{132815785361790091971038013719308421299613872730335862090800}\cdot t^{20}+\frac{2223623677858527732699620540205651471191943788086039355146517614269}{265631570723580183942076027438616842599227745460671724181600}\cdot t^{19}-\frac{33133816142929517779395045598167011696136059073523436290774785939531}{53126314144716036788415205487723368519845549092134344836320}\cdot t^{18}+\frac{4394336570338173213579947431374701550680555009582601346132497130821081}{132815785361790091971038013719308421299613872730335862090800}\cdot t^{17}-\frac{171734420610949170825346187726942967149770479732292599618794882856932241}{132815785361790091971038013719308421299613872730335862090800}\cdot t^{16}+\frac{315447910966628140649994221651226221600689276949437775432764897870631676}{8300986585111880748189875857456776331225867045645991380675}\cdot t^{15}-\frac{1411355535270306041483349235715512892097438735602103328919463800731477812}{1660197317022376149637975171491355266245173409129198276135}\cdot t^{14}+\frac{4836189394910435557572245216364063704038913382586112056233055884480814056}{332039463404475229927595034298271053249034681825839655227}\cdot t^{13}-\frac{317776063575179038123397602804608997826649641420428348388248630293844997256}{1660197317022376149637975171491355266245173409129198276135}\cdot t^{12}+\frac{3195268468832187690605085964667778499921555717918591175238814438598618297136}{1660197317022376149637975171491355266245173409129198276135}\cdot t^{11}-\frac{24430911297459959383882976768295071433059021937605681611600712389113284910096}{1660197317022376149637975171491355266245173409129198276135}\cdot t^{10}+\frac{28125221044460794041571246942411314926601627364971874917305598670588769635296}{332039463404475229927595034298271053249034681825839655227}\cdot t^9-\frac{120147750202952678063807694546127555921927512038554163670820977886968485307360}{332039463404475229927595034298271053249034681825839655227}\cdot t^8+\frac{373598695347422093628974478517494295479624937763773232547717964166340400485888}{332039463404475229927595034298271053249034681825839655227}\cdot t^7-\frac{823889079986629677282188168710203636593635776472454705881887882686374169983488}{332039463404475229927595034298271053249034681825839655227}\cdot t^6+\frac{1244034509533016547124027423828904488116872883994100788158890105693742995371008}{332039463404475229927595034298271053249034681825839655227}\cdot t^5-\frac{1224960723277155160732317072001279106076575998023114671654661279574204488944640}{332039463404475229927595034298271053249034681825839655227}\cdot t^4+\frac{732921866139544361579899671342793216942442039955766232167750282795633740979200}{332039463404475229927595034298271053249034681825839655227}\cdot t^3-\frac{238544658750475285667765539984885106104076563410754208325638260557834069611520}{332039463404475229927595034298271053249034681825839655227}\cdot t^2+\frac{34480526275424085094841634314910585666719796283681091126527618389319079761920}{332039463404475229927595034298271053249034681825839655227}\cdot t-\frac{1312488461864242772447069520840875622006260503882222451514296804273033041920}{332039463404475229927595034298271053249034681825839655227}$

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.