Rule: Q[4, 8, 30]

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.

• $P_1$:
  $\frac{35}{8}\cdot t^4-\frac{15}{4}\cdot t^2+\frac{3}{8}$
• $P_2$:
  $\frac{35}{8}\cdot t^{12}-\frac{87219}{8284}\cdot t^{10}+\frac{102069}{11336}\cdot t^8-\frac{891429}{269230}\cdot t^6+\frac{24664563}{47599864}\cdot t^4-\frac{792603}{23799932}\cdot t^2+\frac{30429}{47599864}$
• $P_3$:
  $\frac{35}{8}\cdot t^{42}-\frac{12273981785066856558647929240429529366716346211529994546281545350477222618487300681520620859723429458631147103097}{285628149246674977278685651271182401226344511628054737418082697916233716494518075757822937542599488518092144592}\cdot t^{40}+\frac{16679278308566959095598712469327418957916270079207675236612451748760942759380979995742991580349167475487737570649177}{85402816624755818206327009730083537966677008976788366488006726676953881231860904651589058325237247066909551233008}\cdot t^{38}-\frac{2461924752567053884163591235891509085007437630762502793391708933132244488930399961969137703909673724721394194804338793}{4517359510941031436703086567301787139816336527456437280023513700544139507264221535518263348255970173802320999430160}\cdot t^{36}+\frac{2990307278030379225223331445012771623585774311400846622184139895209283184951473481620152618867007490638118242086614931683}{2861897828831508116199295443271258879311643068027901564804230046418063849168793150135337106565098970776230430505654032}\cdot t^{34}-\frac{9448598624190141983229532721781001826484248808903930473332241423092778691804537804522443704354178302519825978730457743}{6474881965682145059274424079799228233736749022687560101367036304113266627078717534242844132500223915783326765849896}\cdot t^{32}+\frac{461377697018199973942771921372949039299885619645075180003147952610849203960826459367857481927970170178344354054516331019943}{300373011828977550372270170273926097377164655536987256882467497665966495463495245772292660728751637565146420331159600388}\cdot t^{30}-\frac{106483403252666110422168726943872155521448057683524549196615976989594315558674728532815582773054161220468235707028272370401}{85613563758017755903207439836529660605085578148223421043795083875806875518580770534131724555537906359148013524340175956}\cdot t^{28}+\frac{1594124695692411575667327324094572736281538725662291085326651353228311420572793273376571684546830272143061383907913135675053}{2033322139252921702701176696117579439370782481020306249790133242050413293566293300185628458194025276029765321203079178955}\cdot t^{26}-\frac{96823173633284566316408410375147836620260249946156729107374459731774282191530703046572613920641907077409845169952135412845}{250255032523436517255529439522163623307173228433268461512631783636973943823543790792077348700803110895971116455763591256}\cdot t^{24}+\frac{1984167338094651229673519959038124151498084609972507247334226314203201133736799450924766228825636681499454418565226073772895}{13263516723742135414543060294674672035280181106963228460169484532759619022647820911980099481142564877486469172155470336568}\cdot t^{22}-\frac{10182411680723549502201060749473062835620845300525224932055654069275443192855003138206118971528732406598224326362433355469465}{225479784303616302047232025009469424599763078818374883822881237056913523385012955503661691179423602917269975926642995721656}\cdot t^{20}+\frac{125325505268272056285994907130281707542002522215103933502093351263761914723412883451130170940793740832463704393142605931205}{11867357068611384318275369737340496031566477832546046516993749318784922283421734500192720588390715943014209259296999774824}\cdot t^{18}-\frac{7749834266270112556929711186920967665402827152256295817016229969740845919606544740612249453895746493810354337872231741544}{4101218986946581345286341012169142010909003368600471958078722191050671671476628834625425497458556245012263494021757275123}\cdot t^{16}+\frac{4169304492151460104971815145893944964820477636879792507436852884033481495008063808504568426829383400948720005203749245745}{16404875947786325381145364048676568043636013474401887832314888764202686685906515338501701989834224980049053976087029100492}\cdot t^{14}-\frac{607564347808004759870753116879777301142406450319248964428830831221319852439898734156506621392903304340289660907083842295}{24244849395828235383263934101399248679874501092282986436301709581137522221560692881615445002979222842854821179061517639516}\cdot t^{12}+\frac{1328309214237801490499254400502884282793864566332979681625589456047613489292801543125261297301428838134889239215952591395}{759671947735951375342269935177176458636067700891533575004120233542309029608901710290617276760015649076117730277260886038168}\cdot t^{10}-\frac{1619119883399663678481219235720362854507444713842053195413798558783437012198169548611970464513295910581050121993932863995}{19751470641134735758899018314606587924537760223179872950107126072100034769831444467556049195760406875979060987208783036992368}\cdot t^8+\frac{6722165281377135398910154889125662797351395474930654991542950324755140761747779038272864693700741204598647261727545583}{2821638663019247965557002616372369703505394317597124707158160867442862109975920638222292742251486696568437283886969005284624}\cdot t^6-\frac{1373088804440289059214725880418238341787233831155065198253649680098259041406652620598893631045908603797058751718510685}{36681302619250223552241034012840806145570126128762621193056091276757207429686968296889805649269327055389684690530597068700112}\cdot t^4+\frac{7333629604537765297779292108378135191158823485198405213713984449421717368742686978689002068597788167521345734933235}{30301945641989315108373028097564144207210104193325643594263727576451606137567495549604622058092052784887130831307884535013136}\cdot t^2-\frac{71680516984039435982919510439003235379056923482314554963289187111028293558947116747710868388405661399629312729265}{257566537956909178421170738829295225761285885643267970551241684399838652169323712171639287493782448671540612066117018547611656}$

Warning: This rule has negative weights!

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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