Rule: Q[1, 3, 5, 8]

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.

• $P_1$:
  $-t+1$
• $P_2$:
  $-t^4+\frac{49}{4}\cdot t^3-\frac{153}{4}\cdot t^2+\frac{57}{2}\cdot t-\frac{3}{2}$
• $P_3$:
  $-t^9+\frac{8913807221}{174577516}\cdot t^8-\frac{346896933499}{349155032}\cdot t^7+\frac{3329250396937}{349155032}\cdot t^6-\frac{8538378231899}{174577516}\cdot t^5+\frac{23551735187795}{174577516}\cdot t^4-\frac{8100489458905}{43644379}\cdot t^3+\frac{4370729197935}{43644379}\cdot t^2-\frac{409117906830}{43644379}\cdot t+\frac{10559938470}{43644379}$
• $P_4$:
  $-t^{17}+\frac{4055728404665695424150487561567307142216787970984648823381029355868705734035089732022630232176040887498454045}{22709335132155034484118668651120753194103624874639864020081080858438417419937945649224645053704691414629068}\cdot t^{16}-\frac{5688866074094752280267338940098663660790819613465234215237715766660440197885571792207812059490080626537016056427}{408768032378790620714136035720173557493865247743517552361459455451891513558883021686043610966684445463323224}\cdot t^{15}+\frac{255919100446266938142570773553880797674174456892674998597358321356709535724438239787320949447559368552783095555161}{408768032378790620714136035720173557493865247743517552361459455451891513558883021686043610966684445463323224}\cdot t^{14}-\frac{18529484131849208343760341877469877401181405099240277421653034058987004372305726895886452476474984364242385599576551}{1021920080946976551785340089300433893734663119358793880903648638629728783897207554215109027416711113658308060}\cdot t^{13}+\frac{364843177542174149936486226609141022324672886155479999078451733696636771350674596168338303986241381653214606321824863}{1021920080946976551785340089300433893734663119358793880903648638629728783897207554215109027416711113658308060}\cdot t^{12}-\frac{1257174777551570460991936002612553468472242662190117346012167935491753108861228654358525430961976720186670431681536897}{255480020236744137946335022325108473433665779839698470225912159657432195974301888553777256854177778414577015}\cdot t^{11}+\frac{12306961944008063562008663678168343157400707493571617287246550940593594387619247244531763770152461949034627831360005511}{255480020236744137946335022325108473433665779839698470225912159657432195974301888553777256854177778414577015}\cdot t^{10}-\frac{429658067732297683320900137369458174198152228401050665151644983908998463544044271101420909089141890875313658970382844182}{1277400101183720689731675111625542367168328899198492351129560798287160979871509442768886284270888892072885075}\cdot t^9+\frac{710117866607899456498586515820313798632003793141004287075021981871419654778211005307561830000734013120439690532921528634}{425800033727906896577225037208514122389442966399497450376520266095720326623836480922962094756962964024295025}\cdot t^8-\frac{34745997503847953580804614205740930887511845013922026104271656256503750412436177284635721300040813644327730184478076368}{5997183573632491501087676580401607357597788259147851413753806564728455304561077196098057672633281183440775}\cdot t^7+\frac{5858008830425210844774090709437497058460095171009406513419406311675347317679079229625471299416468139491856283349871395344}{425800033727906896577225037208514122389442966399497450376520266095720326623836480922962094756962964024295025}\cdot t^6-\frac{26910723250350475194329209692752613819083672124731624241051314953370990674591416918123741401709321662906102464686541984}{1256047297132468721466740522738979712063253588199107523234573056329558485616036816881894084828799303906475}\cdot t^5+\frac{580142538900482676931400185802351301109289048536284724503859134427977324034871942058660419681450220623238061525841553952}{28386668915193793105148335813900941492629531093299830025101351073048021774922432061530806317130864268286335}\cdot t^4-\frac{301986809178225440647035215715629848371277238424653124780569317893711054336461775258856310560074285157009792191944277632}{28386668915193793105148335813900941492629531093299830025101351073048021774922432061530806317130864268286335}\cdot t^3+\frac{70113216786054456482631848857422110478206650757427966612277105625214178595056617474836868121826747174262689405013688704}{28386668915193793105148335813900941492629531093299830025101351073048021774922432061530806317130864268286335}\cdot t^2-\frac{5311909685178429765874471191030228972891439995192303057700448015734783784176958450212800420411155763237402306280173312}{28386668915193793105148335813900941492629531093299830025101351073048021774922432061530806317130864268286335}\cdot t+\frac{125149408280716053669664082388714207750132682858323070354983233838598204160979121959126156368713885473805575792292608}{28386668915193793105148335813900941492629531093299830025101351073048021774922432061530806317130864268286335}$

Warning: This rule has negative weights!

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.