Rule: Q[10, 42]

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.

• $P_1$:
  $\frac{46189}{256}\cdot t^{10}-\frac{109395}{256}\cdot t^8+\frac{45045}{128}\cdot t^6-\frac{15015}{128}\cdot t^4+\frac{3465}{256}\cdot t^2-\frac{63}{256}$
• $P_2$:
  $\frac{46189}{256}\cdot t^{52}-\frac{3117683890387936214241687991167000589965476350095125235063088075253411}{1344796007484465419061558419044946555870594157450588201460705966592}\cdot t^{50}+\frac{18870485082245840557383388282668490991886893076613008304967177842562175}{1344796007484465419061558419044946555870594157450588201460705966592}\cdot t^{48}-\frac{81170403093121357621740121320420628988850091331433804788005966124381066075}{1526007269492997134280103416011253104274156720167054961607536095590272}\cdot t^{46}+\frac{61441457882841699320297467727796822570106351181163848368066607166226374375}{433864811914675655824735284944375882587750440047496018496260262471744}\cdot t^{44}-\frac{231956947804207367797206750697846620030338692909093282671104497295004045876930465}{824042908188038790513166324577132668805975112785729567898095086594683153152}\cdot t^{42}+\frac{29648518553331106452027918423378295725920378461516733128817834147520555868451029915}{68395561379607219612592804939902011510895934361215554135541892187358701711616}\cdot t^{40}-\frac{54349261801922724009186172826265217280989906349837325314586679297242878893901731775}{102593342069410829418889207409853017266343901541823331203312838281038052567424}\cdot t^{38}+\frac{2820621070226038526700396174144765747640699367637758217776071853292386840525955340475}{5403249348988970349394831590252258909360778814536028776707809482801337435217664}\cdot t^{36}-\frac{448460766545130619055092184535798432153944727710381843374572001434186400596604136145125}{1069843371099816129180176654869947264053434205278133697788146277594664812173097472}\cdot t^{34}+\frac{1579641215439926463432775571910801099950916057110353412197206788290673831050968161875}{5721087545988321546418056977914156492264354038920501057690621805319063166701056}\cdot t^{32}-\frac{28010822464918747905904112829231751621899046023875488421035040732237409277581827125}{187114422427037398247543978220310673806137027258600617030204028578983696760384}\cdot t^{30}+\frac{12161534769069596700166923219141023150332546677683909858488145669764607542837101625}{181895713890786355192972518381508905520468905301590964932505640357967417185424}\cdot t^{28}-\frac{22501226560954943297780830131764516144827641532354678839640559587412426534076541375}{916215447746183122453491203699452264843843374852458193734102484766058101378432}\cdot t^{26}+\frac{453591123660998208205267318707350522909954219548467951048957682118781196430378562125}{61386434998994269204383910647863301744537506115114698980184866479325892792354944}\cdot t^{24}-\frac{2108641596794372844398524942674995814643528947292022486748171088785108382356140845}{1165565221499891187425010961668290539453243786995848714813636705303656192259904}\cdot t^{22}+\frac{43838422883667535216614308069344893489754174552459708791267210427060127395470721255}{122772869997988538408767821295726603489075012230229397960369732958651785584709888}\cdot t^{20}-\frac{13773665023579605220785687469314739147452520315239935007816453235758240937701127825}{245545739995977076817535642591453206978150024460458795920739465917303571169419776}\cdot t^{18}+\frac{99607334436076985069841433251445661834759367483762989801152836592266139737655525}{14443867058586886871619743681850188645773530850615223289455262701017857127612928}\cdot t^{16}-\frac{6188816200740218737284699663987187191797852620259478267481212452291816772528875}{9539419661827906627898114297341355933962369255816770605349184694328957879057792}\cdot t^{14}+\frac{55071950708591407095718095754764241634019064292665152466441561531169255915170408945}{1215113787587592061766177319319130126382247664795637908963269339525016384878269939008}\cdot t^{12}-\frac{27975973813355230080457568265450979874271986451668741989677453857103759954840255785}{12398059394209228095453830616368450701269136601230358985571753474939739370843524297472}\cdot t^{10}+\frac{30063120610384710964299311667868248082385074288271099983814428424443836868444013225}{398115462769607435509573005347831361407420053083952638536692972695287186463753169107712}\cdot t^8-\frac{309530735176800966719166085742095617725682194829084024013285063630348195796291075}{199057731384803717754786502673915680703710026541976319268346486347643593231876584553856}\cdot t^6+\frac{20320977583986487095815879659616697698239967100491639155414282906305298787566375}{1194346388308822306528719016043494084222260159251857915610078918085861559391259507323136}\cdot t^4-\frac{58979232652266751559377791043217477502164978386578141456314570917284303708877}{796230925539214871019146010695662722814840106167905277073385945390574372927506338215424}\cdot t^2+\frac{42683966396283485863688631944376778769803895714829111758079337432015812889}{796230925539214871019146010695662722814840106167905277073385945390574372927506338215424}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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