Rule: Q[3, 8, 24]

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.

• $P_1$:
  $\frac{5}{2}\cdot t^3-\frac{3}{2}\cdot t$
• $P_2$:
  $\frac{5}{2}\cdot t^{11}-\frac{10483}{1482}\cdot t^9+\frac{1617}{221}\cdot t^7-\frac{69993}{20995}\cdot t^5+\frac{68299}{109174}\cdot t^3-\frac{3633}{109174}\cdot t$
• $P_3$:
  $\frac{5}{2}\cdot t^{35}-\frac{78351457376627706924051418239660072311672526283713276851}{3303089584299048304829211877489769165820100780122779874}\cdot t^{33}+\frac{1079586870209322542335930713217405097342155831107459185004}{10459783683613652965292504278717602358430319137055469601}\cdot t^{31}-\frac{12766990400014114853635941557789919486521649669123508462252}{46793769110903184318413834931105063182451427718406048215}\cdot t^{29}+\frac{19961624957918132692609697227580606247620487814769879154123226574}{40797643613293516821762877171334219049290011241426128240358829}\cdot t^{27}-\frac{93295521685993473619781001105651524668913769060942756878857153194}{148196568680767048284181391434333701674771408355607730787628225}\cdot t^{25}+\frac{174082920757847743014656950585970335210366560168648905240301393108}{290465274614303414636995527211294055282551960376991152343751321}\cdot t^{23}-\frac{44045558187678973253771950230078599684125602745116167558326106404}{102645623359941808179990900593464816528420617576831459850799339}\cdot t^{21}+\frac{23869070778761353776526410781105586620901196749319282271572404517}{102645623359941808179990900593464816528420617576831459850799339}\cdot t^{19}-\frac{6318460980921000250162608469758765235169984306597453495216361}{66351404886840212139619198832233236282107703669574311474337}\cdot t^{17}+\frac{768991311649516040692222228554844555318008032958990631356198708}{26335860812000088456693535196070447294525940679912952777739505}\cdot t^{15}-\frac{53626360751876307259902258308852350031572406096645534152069758588}{8140259660160921459090697061251280726695059288039447156818235469}\cdot t^{13}+\frac{418882684212916561081271725632087943274465239869279260507476739838}{393863332787786122905234496271311967468553253244370173972205393077}\cdot t^{11}-\frac{973834515822379126672658822988639256109667588555305501199068664346}{8271129988543508581009924421697551316839618318131773653416313254617}\cdot t^9+\frac{253615249941997048282065265703262089867321601125511488270897868}{30297179445214317146556499713177843651427173326490013382477337929}\cdot t^7-\frac{52034192605878498770450095234822649956599759962756909495363364}{151485897226071585732782498565889218257135866632450066912386689645}\cdot t^5+\frac{5273690797991418402005988805206880191670981093529770559605897}{787726665575572245810468992542623934937106506488740347944410786154}\cdot t^3-\frac{21215298226446782797527588161855797102226802663824907778593}{538970876446444168186110363318637429167493925492296027540912643158}\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.