Rule: Q[10, 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.

• $P_1$:
  $\frac{1}{3628800}\cdot t^{10}-\frac{1}{36288}\cdot t^9+\frac{1}{896}\cdot t^8-\frac{1}{42}\cdot t^7+\frac{7}{24}\cdot t^6-\frac{21}{10}\cdot t^5+\frac{35}{4}\cdot t^4-20\cdot t^3+\frac{45}{2}\cdot t^2-10\cdot t+1$
• $P_2$:
  $\frac{1}{3628800}\cdot t^{28}-\frac{122482619866131008827723028160340875103818307710426091}{764734686649083924554975811206736964306034487146124931200}\cdot t^{27}+\frac{1626479104672331472680166288408897091513573044569401333}{37764675883905378990369175862061084657088122822030860800}\cdot t^{26}-\frac{201806363597061003147340032222800797475055466447024315297}{28323506912929034242776881896545813492816092116523145600}\cdot t^{25}+\frac{20274118867678934396176318602476993682781690984708352715865}{24924686083377550133643656068960315873678161062540368128}\cdot t^{24}-\frac{11056467254661407607716906687204058148122938701450502977671}{162270091688655925349242552532293723135925527750913855}\cdot t^{23}+\frac{11286558470371087345818347096739667045467002509680913750316189}{2596321467018494805587880840516699570174808444014621680}\cdot t^{22}-\frac{140497504465372914816041884704696984358167000658549739552883347}{649080366754623701396970210129174892543702111003655420}\cdot t^{21}+\frac{1585802643442795551659581781232600522385505476152062182453069989}{185451533358463914684848631465478540726772031715330120}\cdot t^{20}-\frac{1256479176610476681350795533454520392405284177314501297610352975}{4636288333961597867121215786636963518169300792883253}\cdot t^{19}+\frac{11702547221255345801679163462612881183558351420668889795648781717}{1685923030531490133498623922413441279334291197412092}\cdot t^{18}-\frac{669042368578416757645085597897621264564941756577295994582758872817}{4636288333961597867121215786636963518169300792883253}\cdot t^{17}+\frac{22622569947678300991435802599342518429866182288973117438682770474943}{9272576667923195734242431573273927036338601585766506}\cdot t^{16}-\frac{155488331447787277536315349473211141868144862341632369372051625250048}{4636288333961597867121215786636963518169300792883253}\cdot t^{15}+\frac{1734038164698695988124112949644862374620257153109648508013051322418400}{4636288333961597867121215786636963518169300792883253}\cdot t^{14}-\frac{15623882183322119942834302716029619453131566713070670464123983854712960}{4636288333961597867121215786636963518169300792883253}\cdot t^{13}+\frac{113029051188267040160502843540174687550970845044064401267187925728424640}{4636288333961597867121215786636963518169300792883253}\cdot t^{12}-\frac{650994743821919766561777382395511000923977543486925528029994283349479680}{4636288333961597867121215786636963518169300792883253}\cdot t^{11}+\frac{268368239167280251889947717845407884684174612436531546513468809564752960}{421480757632872533374655980603360319833572799353023}\cdot t^{10}-\frac{944545813726009420073781604111918127353118188585662957243794006543712000}{421480757632872533374655980603360319833572799353023}\cdot t^9+\frac{2533332868248816397840711900965950755773821007735076223161114332725136000}{421480757632872533374655980603360319833572799353023}\cdot t^8-\frac{5056507726271663017655180852910014571800941836907464086912393700016128000}{421480757632872533374655980603360319833572799353023}\cdot t^7+\frac{7281170929379904516796941902683102016218304816622712021141198278694656000}{421480757632872533374655980603360319833572799353023}\cdot t^6-\frac{7254089902414178728436322543526910586672458572257422490997029583561728000}{421480757632872533374655980603360319833572799353023}\cdot t^5+\frac{4717258756076447839415785416351867761219120605940905759131415370641920000}{421480757632872533374655980603360319833572799353023}\cdot t^4-\frac{1839631195884877420864320347557780824973174979393334243461885356019712000}{421480757632872533374655980603360319833572799353023}\cdot t^3+\frac{378451157443640260494015325352129832340291987225568824168035979957248000}{421480757632872533374655980603360319833572799353023}\cdot t^2-\frac{33646657197655244676942133491963485479637082276925746711232370651136000}{421480757632872533374655980603360319833572799353023}\cdot t+\frac{877991336003599619440173608098742726163628918768035715284012705792000}{421480757632872533374655980603360319833572799353023}$

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.