Rule: Q[4, 11, 28]

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.

• $P_1$:
  $\frac{35}{8}\cdot t^4-\frac{15}{4}\cdot t^2+\frac{3}{8}$
• $P_2$:
  $\frac{35}{8}\cdot t^{15}-\frac{638415}{40664}\cdot t^{13}+\frac{11181153}{503608}\cdot t^{11}-\frac{55088825}{3525256}\cdot t^9+\frac{19993545}{3525256}\cdot t^7-\frac{160318323}{162665384}\cdot t^5+\frac{10517265}{162665384}\cdot t^3-\frac{64053}{91941304}\cdot t$
• $P_3$:
  $\frac{35}{8}\cdot t^{43}-\frac{3244488800839734480167646753999010401523322222816914359520882508048147950553594335713877784672218371148143133876084821}{68880093946072843602749195490209685131270297056459569494665239257993922904114607039607797601087258885396330016925408}\cdot t^{41}+\frac{66642593907309792308989240485843773998150588702123215943831021929854808300958821014021821804689913273514187787277564153903}{282787225695602059411086822085055862306430204565294762560348139773694050482842519201109813051263741353994632884487262544}\cdot t^{39}-\frac{14203312743852663129622245067413422086749631052046672456548513905879899103061736506881223467292031860022718351038007935590901724}{19529569046948630388453905819834668043051848002404021221050014676340795996187334787205728134245205131493962690985948050870515}\cdot t^{37}+\frac{96848935343255872174914885972871699665490383565795836780806752083488080960488370894192034884796821810433318424883326839468797169}{62494620950235617243052498623470937737765913607692867907360046964290547187799471319058330029584656420780680611155033762785648}\cdot t^{35}-\frac{22153408126791411582187573610744075886354251986829655790005689525029114547073542689347957929502595305589983604022273524754639294201}{9159925870705963327338837655383026016992546765927554638993058312194585916383179653336263801479122498245854043863580662945439264}\cdot t^{33}+\frac{3364342520285327350759379075280401377232506874270838836555559748860123767805350885611547920545801690519009467679655540239217919579}{1175832235086413642608731264685110662955693082326558991958284000513193899199019273681633190004685337527350792667673443686178020}\cdot t^{31}-\frac{36156786915320992618396829347123567490888349978761184925049903206368984113949940692660575002707892289885910822807254029403705023954231}{13798508861962572737377722264206242140851353890410402426529658574422381726490411078581333648023982904417214287034414629001667682502}\cdot t^{29}+\frac{1208814586171346517579269344641924274402443350927358609911219973678892219299636108276507108153844863696964530630326665905342997086868}{642787679905088792113869049574824944449597230919739243471878505019676167383093683784844735156396719149870230762472731164673960365}\cdot t^{27}-\frac{43651999152626747659563734748653291410206636844850176924523308089294827753268041635293147106673362945875337371414415616221592023679}{41021208062319056818662868121014469389376005619949171093362047043990729770317089791397498767815631079649838088545268313643010576}\cdot t^{25}+\frac{1296469880629449491202531816045872459656353677891662429799266139150979934395490716871719589546540652800916067486042770364236514943985}{2727910336144217278441080730047462214393504373726619877708576128425383529726086471127933668059739466796714232888260342857260203304}\cdot t^{23}-\frac{1935646873780954753167782390588553587290537799174889914932141774618229301148776443652860030800375030161612442162215966071272595482241}{11593618928612923433374593102701714411172393588338134480261448545807880001335867502293718089253892733886035489775106457143355864042}\cdot t^{21}+\frac{3335264067294838835288743464574462273054354526965767112066049928351626841834070922336484746720278961564346805245984952925842210338965}{72874176122709804438354585216982204870226473983839702447357676573649531436968310014417656561024468612997937364300669159186808288264}\cdot t^{19}-\frac{184652043739096863549024386980209631233405708596447727226187106660946305947069179650688908102531817923191049899190864947885242044347937}{19108376075965276090099081239526597087550962809867863031196628667890629769419795815359408683527573822629248628891891250056246257480592}\cdot t^{17}+\frac{50689861861914548797622653076755267614757162184979416681513127092971363625304532504921635810483850733511687458970010801999566897332875}{32877647071881430919729301544479586165345038952272646686029493443282407103266413388191923764304796135994442493828695239067364884194548}\cdot t^{15}-\frac{330404745889569363028591332639193925486736555896205940580343556832702528172266133372373000870102877726535247083842796184354701559715}{1826535948437857273318294530248865898074724386237369260334971857960133727959245188232884653572488674221913471879371957725964715788586}\cdot t^{13}+\frac{177214708753930115589628682688443697604327889542103457527269087708162829745108779884392124638888432394814297986302324424988058427253}{11802232282213846996825903118531133495252065264918385989856741236050094857582815062427870069237619125741594741374403419152387394326248}\cdot t^{11}-\frac{75119304408335798615580809634802474516165432404539050139970959937918276681067318448955762204281366357119858436738042756413823339165}{90126137427814831612125078359692292145561225659376765740724205802564360730632405931267371437814546051117632570495444291709140102127712}\cdot t^9+\frac{142078387432598995138032604961440641226428180340986155717110545838665509435730649760277835971762517796457097336773572073664854841}{5007007634878601756229171019982905119197845869965375874484678100142464485035133662848187302100808113950979587249746905094952227895984}\cdot t^7-\frac{45805094110772394458405317777476386023381672101232576236889958578962778730963589044231583595478823262115118014283571902756715}{89410850622832174218378053928266162842818676249381712044369251788258294375627386836574773251800144891981778343745480448124146926714}\cdot t^5+\frac{34121744535394439172887229279556039156122165779516461128949904846826798892814851578561509735896528473395694058930406735172175}{9298728464774546118711317608539680935653142329935698052614402185978862615065248231003776418187215068766104947749529966604911280378256}\cdot t^3-\frac{1555027295356344404263579460322079100920432813252958737605352405556098592961522211940867052567375409428811540335396731}{366041233088926569910103631725537069130361656068482612735032660301882127071673125002608948301896001289826399816935853980944014816}\cdot t$

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 Legendre type can be downloaded here packed into a single file.