Rule: Q[2, 4, 7, 22]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^6-\frac{25}{14}\cdot t^4+\frac{45}{98}\cdot t^2-\frac{1}{98}$
• $P_3$:
  $\frac{3}{2}\cdot t^{13}-\frac{11979409}{2770390}\cdot t^{11}+\frac{54031549}{11635638}\cdot t^9-\frac{751494029}{329676410}\cdot t^7+\frac{11821062}{23548315}\cdot t^5-\frac{193274}{4709663}\cdot t^3+\frac{52009}{70644945}\cdot t$
• $P_4$:
  $\frac{3}{2}\cdot t^{35}-\frac{7651123927412577219188054547294061564920487499977002402769003724663043870809966698303611644248487459643}{593646861531982276591007572438810704830269528136005559877957795133143975686417941950363361589958764030}\cdot t^{33}+\frac{3253858211410930746748106840849962155545348128886783261536759479980059645674305669458406945951958301412264}{64291955103913680554806120095123199333118189897129402134782829212919492566839063113224352060192534144449}\cdot t^{31}-\frac{7734963090972099558904353984980505370581682842253807836173237645210395683240373513428828667798076392772596761539}{64299027218975111059667148768333662885044832898018086369017655324132913711021415410166806738919155323204889390}\cdot t^{29}+\frac{913143505768141606379739915674539032389595709307144100952405175509528983287708376571455903328711575437454345885679}{4725978500594670662885535434472524222050795218004329348122797666323769157760074032647260295310557916255559370165}\cdot t^{27}-\frac{179393200159379779655659778298386620176298552542545494354697662507250252117483008488408028163526077053889059325717}{809129792205237115588369099542815118380464590084598665471757811494984936164373262053514166562604255403642240175}\cdot t^{25}+\frac{513587483407516887258716335917861484660892793673557196300448985444752302892631680507062031477419889799498509995793735}{2741137544841214090705653300667167345444602719704999974938602243470250167340217162254413152914128192286243035575258}\cdot t^{23}-\frac{7306751686007963025766993002367162232913356343357299508944512758518504192974890622424124144086676870232850006445602471}{61675594758927317040877199265011265272503561193362499436118550478080628765154886150724295940567884326440468300443305}\cdot t^{21}+\frac{3485580004795259944900050808229921475466839183839471590097484368622627631165660626401158308156718429404273879351871}{61830170184388287760277894000011293506269234279060149810645163386546996255794372080926612471747252457584429373878}\cdot t^{19}-\frac{415031326633429219700968696584947035204752400718711446834919952951204777329048072877937351573953287435210675939651}{20610056728129429253425964666670431168756411426353383270215054462182332085264790693642204157249084152528143124626}\cdot t^{17}+\frac{1992185419885066157498878190421841430681629075475214028271946084817533817862476946006879442901348517713249847701561}{372799555523517617378146125588303387317211559623745020917125249830651006836407243429116339903181963347200235930735}\cdot t^{15}-\frac{81704485180119082794830003487390322517797537256519094819298931701403997962556388703266778028394964673006664214231151}{79083212378388870566484064774798758562891145514850443770552836330742100250229856572763212904795000491386076715439918}\cdot t^{13}+\frac{585547166716082909418605640325250785125250202945596433808865566255552849185481720207256310392645537137436849560450602}{4151868649865415704740413400676934824551785139529648297954023907363960263137067470070068677501737525797769027560595695}\cdot t^{11}-\frac{32250581585731162774300647780151795800423081836385781745107377939990984844191833893861048919320547392201059980567140}{2491121189919249422844248040406160894731071083717788978772414344418376157882240482042041206501042515478661416536357417}\cdot t^9+\frac{409297041569085719293720973107730570706549371915433156064401794833832695070091896662349135436492806996938032336271}{553582486648722093965388453423591309940238018603953106393869854315194701751608996009342490333565003439702537008079426}\cdot t^7-\frac{4545837869802073574911998598589820258179455762971927941894534756649928440190158039005963326502699178554122716094}{197708030945972176416210161936996896407227863787126109426382090826855250625574641431908032261987501228465191788599795}\cdot t^5+\frac{319281018470661795622251492725140410263016430616434231229999803896425967386133760562177046370113184289624122267}{1067623367108249752647534874459783240599030464450480990902463290465018353378103063732303374214732506633712035658438893}\cdot t^3-\frac{6948505694782294973150945643955778526845043582759806029532725068283916589357915447592590217910627424869973719}{8896861392568747938729457287164860338325253870420674924187194087208486278150858864435861451789437555280933630486990775}\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.