Rule: Q[7, 8, 16]

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.

• $P_1$:
  $\frac{429}{16}\cdot t^7-\frac{693}{16}\cdot t^5+\frac{315}{16}\cdot t^3-\frac{35}{16}\cdot t$
• $P_2$:
  $\frac{429}{16}\cdot t^{15}-\frac{27225}{272}\cdot t^{13}+\frac{13131495}{87856}\cdot t^{11}-\frac{1188386485}{10454864}\cdot t^9+\frac{3595718907495}{77669184656}\cdot t^7-\frac{107404612029}{11095597808}\cdot t^5+\frac{9905616105}{11095597808}\cdot t^3-\frac{264663405}{11095597808}\cdot t$
• $P_3$:
  $\frac{429}{16}\cdot t^{31}-\frac{22823157060610658871115730418540993373758924538995986648144983104868352501100563436229}{106850444857798423761979012169284978564855229384406912107932196628657384808757634384}\cdot t^{29}+\frac{149363049642843434127100931142364507244522960987884793099408772303173303061407185359725416279}{194133902001012511172545617735069645430021344887794308436099309749691886024411526971430000}\cdot t^{27}-\frac{95766208774059187222206676236104995452509452250944047087117556909697919346900477485878481836569}{57815952073708948234757011563247963663066727194176075338321279618417498352677521791750690000}\cdot t^{25}+\frac{2569374073340780228607670407064055509596652731871448434482464578409803496411574344586065611067576623}{1082377064048071116618744794036490187573365245140345840494739741438763460060344099665108007545200}\cdot t^{23}-\frac{30635843759845538552927650335348303269271250199073848899950402712964531531483030506536107121475157}{12834510640886218774135313763278539773597216345537697713376360570420120079766926082985470445200}\cdot t^{21}+\frac{411653767482084348982324965244242341052345674803378424434075677846579523141243915519039612093787}{238033530683102804332334139970579434397542358288167827265626737396262878672369055173164113520}\cdot t^{19}-\frac{465456722765954047326139736845959706965173141039726990103029508287465026791009700389391372265783}{510071851463791723569287442794098787994733624903216772712057294420563311440790832513923100400}\cdot t^{17}+\frac{2844262635109002704577804127222640738829109832954983883065074497757518904115664377664811445525213}{8119143706241296493991128354122537178316171699930026982110747286482613651522235251662799468720}\cdot t^{15}-\frac{42599171104604213689655514039810080439709123677813128175594866074801059706027862540166435608071}{440573689485961825255332546347734575567544200771396812982753728723862756284152300477826327760}\cdot t^{13}+\frac{354941294392592624657944338905215505607961259917449577265197024919975578700740704525862710784621}{18944668647896358485979299492952586749404400633170062958258410335126098520218548920546532093680}\cdot t^{11}-\frac{797480290455978969282307156590022543423801127979542727623595367891325520595501706207769821133167}{325503852222946523077280691288003535967039247242649263555530868485348420029209613271208596882320}\cdot t^9+\frac{917528669745036019053482493829461165453070197902870631628773074221198216058469384979764465699383}{4520886836429812820517787379000049110653322878370128660493484284518728055961244628766786067810000}\cdot t^7-\frac{142446187302151426778149818792633403676437252971547971736275865217455700505876459437645556538819}{14854342462555099267415587102428732792146632314644708455907162649132963612444089494519439937090000}\cdot t^5+\frac{2983734193807702394834605181171038664518854609074078506085209491534411511616888728417665206881}{14005522893266236452134696410861376632595396182379296544141039069182508548875855809118329083542000}\cdot t^3-\frac{579354826196938765947234421232693137268688874678414260426503268116363976609958509564329287}{409302251110615128133138787660857633956314588498450107750111666930624837837945247772519834786000}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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