Rule: Q[14, 31]

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.

• $P_1$:
  $\frac{5014575}{2048}\cdot t^{14}-\frac{16900975}{2048}\cdot t^{12}+\frac{22309287}{2048}\cdot t^{10}-\frac{14549535}{2048}\cdot t^8+\frac{4849845}{2048}\cdot t^6-\frac{765765}{2048}\cdot t^4+\frac{45045}{2048}\cdot t^2-\frac{429}{2048}$
• $P_2$:
  $\frac{5014575}{2048}\cdot t^{45}-\frac{1450202218792702177483938121949407843593950769347919092517575}{53297340413227556067710283148861808119290770595342094336}\cdot t^{43}+\frac{6030931299598811367663312450082763859398945625658060299826663977}{42797764351821727522371357368536031919790488788059701751808}\cdot t^{41}-\frac{686190697975506031878274586932465693526872924842644498841081094185}{1519320634489671327044183186583029133152562351976119412189184}\cdot t^{39}+\frac{190530885757955732304240572334988753810443951890293648971462179295}{189915079311208915880522898322878641644070293997014926523648}\cdot t^{37}-\frac{333718915610896309090481567657739737800395705561985272771438346840821}{203588965021615957823920547002125903842443355164800001233350656}\cdot t^{35}+\frac{40822869147770198406239640887504828451062962381929102006387530934776895}{20007242835306077309787101028118009277607387903013527393932005376}\cdot t^{33}-\frac{1765551432927412409654720272025360598500240400224653918079250111672792727}{892823211525533699949249383379766164013229685171978659954215739904}\cdot t^{31}+\frac{819447991438536868605806252744744728245525431897389054706263188804994105}{541912596050323937282628978966823243828925480552146251315494130688}\cdot t^{29}-\frac{9533736591893603865784735684198390421245144566100864514782908798741791535}{10373755410106201085124611883079187810439430627712513953753744787456}\cdot t^{27}+\frac{87732106443377712987818717625694440167180319629786153161711338279384581673}{197101352792017820617367625778504568398349181926537765121321150961664}\cdot t^{25}-\frac{16906872933833739339855992756915162971845511837742805989534477431424041725}{98550676396008910308683812889252284199174590963268882560660575480832}\cdot t^{23}+\frac{5942943766103494514933330400728340883646867195752063322189587017055532715}{113547518456271135790440045285442849186005506979418495124239358706176}\cdot t^{21}-\frac{1063437937538748941793445546298361773233763154501070841347544667764077975725}{84933543805290809571249153873511251191132119220605034352931040312219648}\cdot t^{19}+\frac{507215972729900407351988516252208758102336141168145617160258393099488304975}{219039139287328929946905712621160595177130202200507720173348472384145408}\cdot t^{17}-\frac{47516502190307408124834631124240464274087105259637796446215686818591500855}{146430938583356586967880795828948488530902133727581462883484887637713408}\cdot t^{15}+\frac{171008868437568211589934243554471691435382395985634800110128165032559264725}{5104164144905572460023273454609061600220017232789982420510044654800295936}\cdot t^{13}-\frac{2274034990960590525741993603422047844936500470661346677389630766623856995}{928029844528285901822413355383465745494548587779996803729099028145508352}\cdot t^{11}+\frac{15899719808177623527665755479130355173327140398477774844176171674658025}{132575692075469414546059050769066535070649798254285257675585575449358336}\cdot t^9-\frac{22890872895290779583412576499808389574470155405427673687753724179925}{6356368798138944533030228461530587297907867039589019203623965946202112}\cdot t^7+\frac{950845621210380875241321454735252964066648445325748779170969800055}{16571961509433676818257381346133316883831224781785657209448196931169792}\cdot t^5-\frac{2362876561400758100145618816110036069729502291360767073831524612025}{6496208911698001312756893487684260218461840114459977626103693197018558464}\cdot t^3+\frac{2494275972526711025997361247951037657244359548956380666879431025}{6496208911698001312756893487684260218461840114459977626103693197018558464}\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.