Rule: Q[2, 6, 8, 12]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^8-\frac{161}{52}\cdot t^6+\frac{105}{52}\cdot t^4-\frac{245}{572}\cdot t^2+\frac{25}{1716}$
• $P_3$:
  $\frac{3}{2}\cdot t^{16}-\frac{52675}{9724}\cdot t^{14}+\frac{62424565}{7972932}\cdot t^{12}-\frac{25786918405}{4472814852}\cdot t^{10}+\frac{2493674299078805}{1096541870671764}\cdot t^8-\frac{66130895817287}{143027200522404}\cdot t^6+\frac{613871878555495}{14255044318732932}\cdot t^4-\frac{244523487906245}{156805487506062252}\cdot t^2+\frac{24672636591575}{1411249387554560268}$
• $P_4$:
  $\frac{3}{2}\cdot t^{28}-\frac{8316938064028842666512436925585280529142464577044888948379339235506771837211919063261319}{804990331875215652569152505939395056619561154818885920408009599703475202981730088816108}\cdot t^{26}+\frac{102599185326412392242345704582502242729542814968166005768273127744680272935163794800657686513675}{3234807764191637212556942903424620489507479185653868394662123319861232005095512403292467479844}\cdot t^{24}-\frac{18503840811673336215368685754202515852485511796875431653871153415998675318950657584325181887028571900}{323475115505576385890572315692381055864891280476811945196521673270313443353542323182540986166310273}\cdot t^{22}+\frac{13449127258632999808273814772126681567525180002553599241001652637685296736023745139365198341393693539835625}{199979432858088444438041398151975201118904817198935634383284021892519717576913642122556853549708669594606}\cdot t^{20}-\frac{3413741780855649237632735394090894527848555087007045552610935991818097943545844141525929257846607253668775}{63151399849922666664644652047992168774390994904927042436826533229216752919025360670281111647276421977244}\cdot t^{18}+\frac{9567051197229501097143167079122717453745058592594685663993135060320865804487730733072727139266717919150800625}{315777224207735203981174682383427194305091870987055744374194133467183317672859040231620223429001172269729052}\cdot t^{16}-\frac{30881397560239081355005429060470292423934099292524600995118426207093390832603955691784080223685296167151584500}{2605162099713815432844691129663274353017007935643209891087101601104262370801087081910866843289259671225264679}\cdot t^{14}+\frac{11505882996717241711904222688514270568002887554794897731681433912638915292912831481160745028892557293506390875}{3607147522680667522400341564149149104177395603198290618428294524605901744186120574953507936862051852465751094}\cdot t^{12}-\frac{124899211043245572651707059042693609334023709669248842341451397977464931938038455958709621586099340597781125}{218615001374585910448505549342372672980448218375653976874442092400357681465825489391121693143154657725197036}\cdot t^{10}+\frac{35972144127173264687446184918800696538120488203255773890518697083383746025060569455368430004172021785463053}{558682781290608437812847514986063497616701002515560163123574236134247408190442917332866549143617458631059092}\cdot t^8-\frac{1442874141446523528794006287021204640287585477231598382581554558967076196155667357463987349426697805578216}{346140418843094358210133786458756732219043012428118796717866646300566328987557024869276014143328208064895307}\cdot t^6+\frac{2806180326903775561350493194445073765945551270484795362522317967053571147096714131903660293307462992654045}{20821677502715368316948047770057520353483971978368376848720901339003297636020737957521064850775589131288317698}\cdot t^4-\frac{345843675475622757269469804544100318166524194264911222581398853178690949548843933311353434766443975665}{188387756085349579946867848980917131141601880792568541259741364626175294700106433208055104786045232831514764}\cdot t^2+\frac{42483653113362795211218119635817309259463448459789218587187041411988354484606455336978262791752474180775}{5758140269387286401832360119683179719572567523472418397618998352113457400797734987889007206914485648852642039756}$

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.