Rule: Q[10, 43]

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^{53}-\frac{103128382686849817924591223143879150660029802443198503334549353379937653}{44484035155626648472797956783992844975660912507121108885889672282880}\cdot t^{51}+\frac{592995304756944187002347089386473989576723272111923640133290148998579615}{42259833397845316049158058944793202726877866881765053441595188668736}\cdot t^{49}-\frac{6743502164833404117087302281572987430558880461594214726195541547432207915}{126779500193535948147474176834379608180633600645295160324785566006208}\cdot t^{47}+\frac{18109138145553909468827363799221839937877526111908358591868493511218139077405}{127878255861879926364752286366944231451532425184221051714267040911595136}\cdot t^{45}-\frac{32359861681084059421187726018392494368032127259138750238739625575239379783767965}{114962552019830053801912305443882864074927650240614725491126069779524027264}\cdot t^{43}+\frac{423586274145377867508348992619981107651755508417633672675633109539810459005993957}{977181692168555457316254596273004344636885027045225166674571593125954231744}\cdot t^{41}-\frac{42965333148411855880091490264832706312361066911126397472965084606454937560801400745}{81106080449990102957249131490659360604861457244753688833989442229454201234752}\cdot t^{39}+\frac{8913302291943984883828048036712340163069294182462270629131985181449706372357477165}{17074964305261074306789290840138812758918201525211302912418829943042989733632}\cdot t^{37}-\frac{137537035779449259127998574706342844619269494501536181605806629051050692750162227245}{328116205974070914381815832090235023556509223903384766776480759175772045962496}\cdot t^{35}+\frac{2442451455222085163329988772775608958360924980280770197981373176143136172851844275}{8846270259104853083823466061256336419415689860140275574856098899346795356832}\cdot t^{33}-\frac{120384075926580455332177265856436538989193376294826952062597612608104317622487475}{804206387191350280347587823750576038128699078194570506805099899940617759712}\cdot t^{31}+\frac{2279002517272143438410024640498773807767771758219709285981525814778827431600774975}{34087973960304331237959045174459900454874535120892440191674234468450701169728}\cdot t^{29}-\frac{75905684887407715869021333047655072933081368026172511591505281535988860643230125}{3090991253105501299993732065627909236648904206364448599755901209782886057536}\cdot t^{27}+\frac{11418510761087516304947929975146214641889077183973591617625529897293979801973775}{1545495626552750649996866032813954618324452103182224299877950604891443028768}\cdot t^{25}-\frac{561881820414182563979313521080100042605891706045457486245364015154845495169726705}{310644620937102880649370072595604878283214872739627084275468071583180048782368}\cdot t^{23}+\frac{295689160389285918287263766435583191453112314320634926463468729358431736004626481}{828385655832274348398320193588279675421906327305672224734581524221813463419648}\cdot t^{21}-\frac{46438682068170663992153112171915866582017273672583049039812007978927547378386835}{828385655832274348398320193588279675421906327305672224734581524221813463419648}\cdot t^{19}+\frac{83914827919941225895198590781103007629955217876212753935439610506677712215965}{12182141997533446299975296964533524638557445989789297422567375356203139167936}\cdot t^{17}-\frac{6945088451392866454005673964015730264088415284216532518634861722949190494355}{10727557878424975099978246580708626174252079304441321610917539492775898670272}\cdot t^{15}+\frac{3958719734401730162338860604630467100581904520702593886621796075212630356186005}{87687058098245746467222187550712310348336496234503362847639967813950195730803328}\cdot t^{13}-\frac{6280471834261473043902786642158191623361061608578213990605748699087060612944352511}{2803969056807604234782363891309127548008756140090714033778983250786685408883898019456}\cdot t^{11}+\frac{1054070285830261146319009558468126257490319217221321096447380762319920814374385}{14161459882866688054456383289440038121256344141872293099893854801952956610524737472}\cdot t^9-\frac{363467395235253246989527927104485111550488920992649707347241341795359555652215}{240744818008733696925758515920480648061357850411828982698195531633200262378920537024}\cdot t^7+\frac{46008207875571779514028412422312791838804015234283580090930413454204985523905}{2888937816104804363109102191045767776736294204941947792378346379598403148547046444288}\cdot t^5-\frac{813920311334575933121137372701794459244720469080256351522026680190503081}{13191496877190887502781288543587980715690841118456382613599755157983576020762769152}\cdot t^3+\frac{1746031887140791218505198729532309980312796739149045142456242203507853}{150465511255458560578599072450300405038348656507393114186372207270750163986825335640}\cdot t$

Warning: This rule has negative weights!

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.