Rule: Q[2, 6, 37]

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^{45}-\frac{157543480808011278868201576362854900425409323721740015894616339}{9579292742070825975592936657166888462542348075011902328019768}\cdot t^{43}+\frac{427307252869453480345776877800386878224033934040580316123625919303}{5081130564472710978196653401151522408774248343217027620562485512}\cdot t^{41}-\frac{42461252613583296221710742082721221927735998239272800879297886979201943}{159405228068637888807985410500925561008065719023404590512286295482464}\cdot t^{39}+\frac{3768877948257858489248474665005546919770454722290606216180708040596150131}{6437518825848837817245564654845070733018038652868262309150023471407200}\cdot t^{37}-\frac{848468705166004665120442265613234085355862607298210244395867552873562993}{895121665308505067921764228197505073352984422208348854415146120786144}\cdot t^{35}+\frac{372221022925769685126985611108084750074518098153221991935189790251049143623}{317768191184519299112226301010114301040309469883963843317376872879081120}\cdot t^{33}-\frac{187639728353711492259575643864025388208387802476349228777005356308717983269}{166106099937362360899572839164377930089252677439344736279537910823156040}\cdot t^{31}+\frac{94184014885447669333461339565859574843491279904596855349779475100030500141}{109261936704941020002664321974885342513126936492360001844464628577924520}\cdot t^{29}-\frac{36728411885152327998957425860128389819507976929571139854513294554203865473511}{70005683731665782101707069151051537310196330024033515467489122738855924600}\cdot t^{27}+\frac{91754495980938392341884184773926173323727503805550896329228937517287131933}{359003506316234780008754200774623268257417077046325720346098065327466280}\cdot t^{25}-\frac{6108067988627205407401629850356194632054040766572899994068523962414320289617}{61317798878812900425495217492305654218366836759512433035113549557931240624}\cdot t^{23}+\frac{695173208534895344440149636922106840070135221925680799944497558889464072791}{22470497725776156056547936845006419868842505396343065522184468471540019856}\cdot t^{21}-\frac{170699302089972207313399282497395342988196732833085531612009228034810226113}{22470497725776156056547936845006419868842505396343065522184468471540019856}\cdot t^{19}+\frac{23409457865059101473836913142626662383590402470573315881014856269730797587887}{16066405873929951580431774844179590206222391358385291848361894957151114197040}\cdot t^{17}-\frac{127877653066571978080295913844196667866850364940089229584636135282057321979277}{596063657922801203634018846719062796650850719396094327574226302910306336710184}\cdot t^{15}+\frac{2015472314200485851588787364152860052185668574633273238456659504321992779675}{85151951131828743376288406674151828092978674199442046796318043272900905244312}\cdot t^{13}-\frac{21682067849228596885054114491950727743367060448830835865627158351833433107}{11462762652361561608346516283058899935593283065309506299504351979044352629042}\cdot t^{11}+\frac{1007621817899186235183190834942706707404058107296722563007305951052926973}{9657487612360957155303466983678304939334673824550134628775753651998955223956}\cdot t^9-\frac{14488643309895385137345021096454659925613606290629180371903790741693985149}{3918180688443588331580263747663769432530067665960340335103305767382433262290720}\cdot t^7+\frac{58885308032635671885003563469416494492444399066194465835760977337486781}{783636137688717666316052749532753886506013533192068067020661153476486652458144}\cdot t^5-\frac{1585032911526683231146809408935779784489953609715778609655624174107}{2219932401384469309677203256466724890951879697427954864081193069338489100448}\cdot t^3+\frac{141781661415302928922317147641652747070678308676356891805459368617365}{71310888529673307634760800207480603672047231520478194098880164966360285373691104}\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.