Rule: Q[8, 34]

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.

• $P_1$:
  $\frac{6435}{128}\cdot t^8-\frac{3003}{32}\cdot t^6+\frac{3465}{64}\cdot t^4-\frac{315}{32}\cdot t^2+\frac{35}{128}$
• $P_2$:
  $\frac{6435}{128}\cdot t^{42}-\frac{286094818370013242090772500234309316720147}{550137279426976141076861937602324405120}\cdot t^{40}+\frac{22811731046233409795677132680121155810987867903}{9136404868083506262933984628730602558030400}\cdot t^{38}-\frac{4719666458351410015212305935419364832017200013}{639098271560521127752032422305293380906560}\cdot t^{36}+\frac{21534428004518514996795540843888593419568046166996381}{1429738247076929904274371268522773317706921694080}\cdot t^{34}-\frac{717383389665944684068157313640437599463183998992194979}{31930820851384767862127624997008604095454584501120}\cdot t^{32}+\frac{1316237942236569928645802859593554211659879770317982563}{51887583883500247775957390620138981655113699814320}\cdot t^{30}-\frac{77493444286553063613474032748279148718434867319632183}{3500661581345593927913167283217772375532408533200}\cdot t^{28}+\frac{6598145561573480989164818289071523522762015008124587313}{436571395433588291632193217631514190477508370851520}\cdot t^{26}-\frac{22527372048060281737349787117304964883956037643764463899}{2773907481754953299139935367412544010264783956333504}\cdot t^{24}+\frac{29615662175250880720096240622065697679969109962606467}{8614619508555755587391103625504795062934111665632}\cdot t^{22}-\frac{9841340616186557509066199746844853908903923242039321}{8614619508555755587391103625504795062934111665632}\cdot t^{20}+\frac{22124695444238835073703717274415539634693293717090597}{74848333434992630513398113467500678415657035783360}\cdot t^{18}-\frac{2333551657700883815590253447906319625289836792841669}{39702159474213482272324216708848185942218079850304}\cdot t^{16}+\frac{30017590302230539714063936921651752491328706216617}{3407274880249664523371108150386224912951551628944}\cdot t^{14}-\frac{799379653032992909300170560248816493686913449563251}{825346815223553352622739966582017096221879698426512}\cdot t^{12}+\frac{72919559584591226209252145582762132727640429584567197}{970607854702898742684342200700452105156930525349578112}\cdot t^{10}-\frac{502016944460493173790442772363997756031687138329656997}{129183283518790570752511259569417315900648610397717658240}\cdot t^8+\frac{1588287830425756719637448341563599377821082892925255}{12918328351879057075251125956941731590064861039771765824}\cdot t^6-\frac{345684391748415199391757487212717285704177490751313}{167938268574427741978264637440242510670843193517032955712}\cdot t^4+\frac{4595330573920825145463004006581280200651304763931}{335876537148855483956529274880485021341686387034065911424}\cdot t^2-\frac{31534952433554567854034276737927190763506085}{2086189671732021639481548291183136778519791223814073984}$

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.