Rule: Q[2, 16, 20]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^{18}-\frac{318937}{47234}\cdot t^{16}+\frac{9281490}{732127}\cdot t^{14}-\frac{272844390}{21231683}\cdot t^{12}+\frac{132075125}{17371377}\cdot t^{10}-\frac{25545611}{9650765}\cdot t^8+\frac{115155586}{221967595}\cdot t^6-\frac{6801938}{133180557}\cdot t^4+\frac{3276767}{1686953722}\cdot t^2-\frac{20605}{1686953722}$
• $P_3$:
  $\frac{3}{2}\cdot t^{38}-\frac{536111230656915522513849288468023312741957989709031138200067042440549}{37608671004582230394743846909144862523665676591407548490924040459798}\cdot t^{36}+\frac{10389751289161822258970970390543663349697955654388848903998809771168283095}{166719238563313027339899473348239175567409944329709662460266271358284534}\cdot t^{34}-\frac{230295590795155557360187686944205912568195504289475565947359313348202220865}{1386218004557896430119863453224170487759793173482690829826969207307694482}\cdot t^{32}+\frac{441347134801433587963258738007787265668218656467006060179940851571951651273550}{1462303486324195164824668216632587458241189563311103682954407533315244229133}\cdot t^{30}-\frac{99729268227898024626663571677029266041713137378704855674821860473286700731574}{252121290745550890487011761488377147972618890226052359130070264364697280885}\cdot t^{28}+\frac{6232994701952284472594622538923543573576166919968632223315566903746324153823965826}{16140608939192921469397003072449191830980860426468362879672219381088969602150345}\cdot t^{26}-\frac{6460378437805593496210887359291830718061261062277193205246513796734455730286729710}{22596852514870090057155804301428868563373204597055708031541107133524557443010483}\cdot t^{24}+\frac{1689210353175614869859982565924625699077307833999860533340923892066055325439741750205}{10434833502627618543350078151542435348329861131536029347956439081094101069661493041}\cdot t^{22}-\frac{227360268913134446017154205729686183005429996823260312906892522636255978169768233983275}{3239270457315687870671388546185958858845826891261113110444191731888211660624917768299}\cdot t^{20}+\frac{1194791885372725442665333428009147955648479870905934680125296849833816117281494647101}{51542859173933833927451714933191511829860158612477931989932059381330173302477271711}\cdot t^{18}-\frac{12770863994550535825439402124489012916485092236352540293042636936045017001809419988331}{2216342944479154858880423742127235008683986820336551075567078553397197452006522683573}\cdot t^{16}+\frac{16399721655682413577292214702936394030340123141452133677082125396441609559815926429930}{15514400611354084012162966194890645060787907742355857528969549873780382164045658785011}\cdot t^{14}-\frac{781586923501927314497587698089167565120678769398385259818092643449779244470488978710}{5626101320600931564850306422322981175890120390085091191824122481700578147401172965993}\cdot t^{12}+\frac{1388956922829672279462715931389502681646120348311313932998200474436741536077757455950}{110987635142763831779319681240371537742559647695314980784166779866275041635095866692771}\cdot t^{10}-\frac{775268422568939016759931709028476098616471120281503293160335869163151073277057149146}{1072880473046717040533423585323591531511409927721378147580278872040658735805926711363453}\cdot t^8+\frac{43532213791685594653101876109927597521462494196641541654770919402508212141484433}{1813830047416258732939008597334896925632138508404696783736735202097478843289816925382}\cdot t^6-\frac{115502770612195480104389166953162191785321619527557891256289287265631008286158685}{306537278013347725866692452949597580431831407920393756451508249154473924515979060389558}\cdot t^4+\frac{12502067470602887465791360534756915331534549330581018016554350878507075459636745}{7050357394306997694933926417840744349932122382169056398384689730552900263867518388959834}\cdot t^2-\frac{1241929895303352859318060108235254971843144714451271318815643485778654025}{2597500092639420203396709732888695286817097719746494462562780427045805360372243616985202}$

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.