Rule: Q[2, 6, 40]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^8-\frac{161}{52}\cdot t^6+\frac{105}{52}\cdot t^4-\frac{245}{572}\cdot t^2+\frac{25}{1716}$
• $P_3$:
  $\frac{3}{2}\cdot t^{48}-\frac{1748741060645123232402649784228044173776349845625822583131818688560717177}{98444697432338868075210732044940888518502977496663299119441435214487604}\cdot t^{46}+\frac{1154558256638138372815834781467726515234915200798176403834832845612279737335}{11714918994448325300950077113347965733701854322102932595213530790524024876}\cdot t^{44}-\frac{1498995442510175690342255285055293474034081412415391228707777226719497310043945}{4404120429030543941080702519494520529652267704268226012706451487190531940148}\cdot t^{42}+\frac{1547691796730430787918839097105024790271655700887038391377907791098533727942225}{1887480183870233117606015365497651655565257587543525434017050637367370831492}\cdot t^{40}-\frac{95130844639133607553163844642837584725256436635277556882463049046143373128431403}{64997074024044181460125093227265286498054895899255247638074333486778949402404}\cdot t^{38}+\frac{30128519714123408107782980892369683928987613002723157247887602564615274391606636981}{15014324099554205917288896535498281181050680952727962204395171035445937311955324}\cdot t^{36}-\frac{4637162806510898554790304526586849036855851350807999681245555805291491776188494675}{2144903442793457988184128076499754454435811564675423172056453005063705330279332}\cdot t^{34}+\frac{518376311636222650099873198634556784520690046803206272344059807546362418353103565}{279105082573836779211125400328845053785765141214449004563495667325580194492676}\cdot t^{32}-\frac{38154757512977265515352907647375928755826833474403253766752775129452629363718574485}{29724691294113616985984855135021998228183987539338818986012288570174290713469994}\cdot t^{30}+\frac{77161662009985527703178559910009090175939981435988597401699509431449145263425515017}{107623882271790682190634820316458959102045472125192275639010010340286224997046530}\cdot t^{28}-\frac{37079610654545429141380337315620548961572558320696138704918795394992869281608761501}{114457144638253582647183062876234131108524549720442578854185249092050429758763770}\cdot t^{26}+\frac{2704700009965451831245165971509395864564752763995119471642256923823900044578672005}{22891428927650716529436612575246826221704909944088515770837049818410085951752754}\cdot t^{24}-\frac{503906254229264386728519266979724212234446202184030071316940547385325279636882615}{14567272953959546882368753456975253050175851782601782763259940793533691060206298}\cdot t^{22}+\frac{146260206875360053995481199944563193435590914563592025997850748733006472999194429275}{18152903139627018207843233772170733193811993585662193006273780505999198159739933922}\cdot t^{20}-\frac{1578486588505369661081211485513006582204404723146630184724295955879537742112795008953}{1071021285237994074262750792558073258434907621554069387370153049853952691424656101398}\cdot t^{18}+\frac{92265319846143415785832466567499725516989782169450616196339607028766571950284584}{443670789245233667880178455906409800511560738009142248289210045507022655933991757}\cdot t^{16}-\frac{214310262917987143302885680797041160522699917385714118636867279242335892866522416655}{9702192819214769849203742473761369517586810218783922685588445275147571439964531742076}\cdot t^{14}+\frac{3095589607456071154902326936256853429864752474266954260405700495828938407083777365}{1812497559633528433367732110482893206582151359553040501703335930522073785487879556212}\cdot t^{12}-\frac{40844381625889307482253798155774648718553073058718995359162057411683804185076544025}{445380082153584305035725444966841848853777738624715316009465183654651403833976221858276}\cdot t^{10}+\frac{1365776405825990380794766899415548208145246928014131272089802418958844754009270623}{427914196578933940132363662811279423408531552796295107538505764687802329173820291589324}\cdot t^8-\frac{47592989987378495171312026709539717600389442063144955557847157475560854887761}{736513247123810568214051054752632398293513860234587104197083932337009172416213927004}\cdot t^6+\frac{653993072564087525803268283671609686465695793551964719490965476739214834111755}{1039220191691696711750026038255964313992148056791002404022085428527519942279277851002644}\cdot t^4-\frac{2020791115246856314738534439216138317275313024075731857640856756878769315995}{1039220191691696711750026038255964313992148056791002404022085428527519942279277851002644}\cdot t^2+\frac{207431966103342539127447049204081341141450529623452107466044770387830725}{661321940167443362022743842526522745267730581594274257104963454517512690541358632456228}$

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.