Rule: Q[6, 41]

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.

• $P_1$:
  $\frac{231}{16}\cdot t^6-\frac{315}{16}\cdot t^4+\frac{105}{16}\cdot t^2-\frac{5}{16}$
• $P_2$:
  $\frac{231}{16}\cdot t^{47}-\frac{2164828640580126870979931546298319991474991815}{12963249988326980225401202901035706786846224}\cdot t^{45}+\frac{199006895554308524582097501613907197063790431335}{220375249801558663831820449317607015376385808}\cdot t^{43}-\frac{3262874404421463266208574887286508895297673822365}{1075949749031139358708299840785963663308236592}\cdot t^{41}+\frac{22872008984181352529647983682163763033456245273665}{3227849247093418076124899522357890989924709776}\cdot t^{39}-\frac{17675488845149054099035476567562396066824120878473893}{1445000512948820158745246686175549199822961743056}\cdot t^{37}+\frac{4420055070183256900108982823520937914996013894776415}{273378475422749759762614237925103902669208978416}\cdot t^{35}-\frac{115334499260751012475391813375811547394224995314035}{6891894338388649405780190872061442924433839792}\cdot t^{33}+\frac{1153532026757250098004031856236378537507696055073875}{83851381117061901103658988943414222247278384136}\cdot t^{31}-\frac{161765736742169400359006250103324917960409810765647023}{17860344177934184935079364644947229338670295820968}\cdot t^{29}+\frac{44294667407252513247129115066733776839262344394802773}{9238109057552164621592774816352015175174290941880}\cdot t^{27}-\frac{419086166291961787610774688971646333913299728539665}{205291312390048102702061662585600337226095354264}\cdot t^{25}+\frac{9583815421308545525919779532439892299333016485960545}{13754517930133222881038131393235222594148388735688}\cdot t^{23}-\frac{18234061844111550504920398111282709796960070535537015}{96281625510932560167266919752646558159038721149816}\cdot t^{21}+\frac{34031127313985935075464626171009459098528984011892005}{839025593738126595743326014987348578243051712876968}\cdot t^{19}-\frac{333779343063542139627806813437765266077005365872562543}{49502510030549469148856234884253566116340051059741112}\cdot t^{17}+\frac{84361587924157552706138969091043712898392480203503845}{99005020061098938297712469768507132232680102119482224}\cdot t^{15}-\frac{94889215817508256048482294004415943354664888545255}{1192831567001192027683282768295266653405784362885328}\cdot t^{13}+\frac{521945831756452329797450418008644999118402323094165}{99005020061098938297712469768507132232680102119482224}\cdot t^{11}-\frac{1182483376935117506506383273539235641907450322139015}{5049256023116045853183335958193863743866685208093593424}\cdot t^9+\frac{1643154253689171844111971229680296534177754589352079}{257116037098673942759159283988813022408270225204295335728}\cdot t^7-\frac{3401897994027845391600901148640440167414108912905}{36730862442667706108451326284116146058324317886327905104}\cdot t^5+\frac{5471490145562668335362031314198459062903168245}{10236469861071327931863484374261876770352678755206137488}\cdot t^3-\frac{321704907648516159753301321045038226699421145}{624424661525351003843672546829974482991513404067574386768}\cdot t$

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.