Rule: Q[2, 6, 8, 14]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^8-\frac{161}{52}\cdot t^6+\frac{105}{52}\cdot t^4-\frac{245}{572}\cdot t^2+\frac{25}{1716}$
• $P_3$:
  $\frac{3}{2}\cdot t^{16}-\frac{52675}{9724}\cdot t^{14}+\frac{62424565}{7972932}\cdot t^{12}-\frac{25786918405}{4472814852}\cdot t^{10}+\frac{2493674299078805}{1096541870671764}\cdot t^8-\frac{66130895817287}{143027200522404}\cdot t^6+\frac{613871878555495}{14255044318732932}\cdot t^4-\frac{244523487906245}{156805487506062252}\cdot t^2+\frac{24672636591575}{1411249387554560268}$
• $P_4$:
  $\frac{3}{2}\cdot t^{30}-\frac{811032515836313108831874283311849972300045086125271882715402738549530952555354985356034209644539283875362192511}{78225999154237587345921416116386677399838830466368848925702381485407983260059413884080673359780164779547539548}\cdot t^{28}+\frac{1095280343285274634868434914015376636175251798192118149788987335340537507350108224289709804974334207772941626337243541}{34186247924385756184327231349767189370600165851582047988661529054371511436327904996207051791017767831793086185727412}\cdot t^{26}-\frac{560159882158493931085368032305402621536533228536388004444212021866115387505092310267244924822367305214057258509960795625}{9589242542790204609703788393609696618453346521368764460819558899751208957889977351436078027380483876817960675096539066}\cdot t^{24}+\frac{5090091508133969127001971878047485286831021815653929594651172102298341540616762828071225933691251782528694138790592003523317225}{72876967955947363936535701187577344210595179267315267856555358636775521169172428503926452009714035859460884341963909061904222}\cdot t^{22}-\frac{2288684500234547006106951861308426010261516202827619792313421272555476887989123654173267380418515220225217743787812304684563075}{39751073430516743965383109738678551387597370509444691558121104710968466092275870093050792005298565014251391459253041306493212}\cdot t^{20}+\frac{85558999509788442767639431515996384923105259768990889268402866100327745864583018451379941727815595755513782898136686116992123925}{2554529508350576020091198788996132170750336283791156231182414150110131426245728283348158791498397256968470998513050707117274308}\cdot t^{18}-\frac{906281004113461723572317666132889498148302734432117738265879195558387131561920322822742455469085872991529514556271454516518723875}{65474427888867868384232915366328969330702246646320386670469523461809675738709957275488919613470358452299732161234825803662687574}\cdot t^{16}+\frac{264454770394716336639617157382103647808571420235878204722412516033011783348814486999427979566596099997334358893228099958940397875}{65474427888867868384232915366328969330702246646320386670469523461809675738709957275488919613470358452299732161234825803662687574}\cdot t^{14}-\frac{11697918985342588686029415496926589631377928503506043384154041097216211685978873048868791967495271350201420787351547313609655125}{14314247392707955031370758825027386007521948659519436761964997032136528299151164748487456109827527758802370593954172442906012668}\cdot t^{12}+\frac{915645956338294472576493172999283400955426912425147424883041128376011308194629268884094884896272508357747416325477627384104991}{8241536377619731684728618717440010125542940137299069650828331624563455687390064552159444426870394770219546705609978073188310324}\cdot t^{10}-\frac{101802133032660987202692118436331352985640272207161547570302444778351383510347123640801590156757253609799351005467183269621733}{10530852038069657152708790583395568493749312397659922331613979298053304489442860261092623434334393317502754123834971982407285414}\cdot t^8+\frac{686006538213074035014469343736371097568101649395544056962144005974031260339469894353457272376242653820833969957821753786387}{1373589396269955280788103119573335020923823356216511608471388604093909281231677425359907404478399128369924450934996345531385054}\cdot t^6-\frac{1480186639197233297911305518100503128085810872599478664019759672996031674129328905196206024467089183907892938421803919088775}{109137921121812810491709284227917709844311055757566467800363058179825155617862369978596279228556439835937633647016982363130048836}\cdot t^4+\frac{126138972210145923846385835208292897217252988823667341241777812138533913802587414016250293981367502294532374050159795732817355}{795942858741380826916035809874203857894560529639932249668047783305464859921070264253902664413862115723493162187694852374307446160948}\cdot t^2-\frac{586370730140249328090727542962220909289733297406352874295724661938432327994619008928997210474089691576649149246584889429925}{1193914288112071240374053714811305786841840794459898374502071674958197289881605396380853996620793173585239743281542278561461169241422}$

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.