Rule: Q[2, 7, 36]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^9-\frac{151}{50}\cdot t^7+\frac{1281}{650}\cdot t^5-\frac{651}{1430}\cdot t^3+\frac{56}{2145}\cdot t$
• $P_3$:
  $\frac{3}{2}\cdot t^{45}-\frac{26586068496872073074123759863344482469672626157273780446802265052593508420498263}{1597767476645688290825084585167828481165798695056506599856639915970332068166900}\cdot t^{43}+\frac{30683451118009559634414999809455534767294964588320085048501101868381973006056737115761}{356076862077781446804987525565917087484128731381598004337450915033232234379607167100}\cdot t^{41}-\frac{356600836283814516390607381132641575305748549558228956360243844674284942796767323200055277}{1288642163859491055987249855023053939605061878870003177697234861505267456219798337734900}\cdot t^{39}+\frac{4589853657664877006499311899532788896592204063615139758089733628206521169187485842285109129}{7434474022266294553772595317440695805413818531942326025176354970222696862806528871547500}\cdot t^{37}-\frac{1482176937578988682830724929999378286061531870052563482786188820664523313532663810405858316}{1458915601143654576412364134874115037083894496859649999564177185016819545658270450599375}\cdot t^{35}+\frac{296808275039090793360836242127299253738282130503841259807557175629482529844887538809365489}{232265695343015097481635693371278639900300310132954043330253452746619878480568047867575}\cdot t^{33}-\frac{1554890646208623332768789827894766663801850770241648189773858388109317508938213000550609519}{1237615156710435284821501627142560963926233617336004389240676022406476009381795140690275}\cdot t^{31}+\frac{8636942381990050639011260703269084219481873783796034636571826668896312206200990953767867044}{8821299521233953625855383938143785593942303442714073838204818457578073683891518555983875}\cdot t^{29}-\frac{98603480003976748646520878738238496965718647950280526681496483191095143280151757216205183956563}{161694420224218369961929187586175589936962422104948973454294322327406090625731535131184428750}\cdot t^{27}+\frac{8842533383842198308943847711460294322548824775922144628494846280373299454125918045778808876599}{29022075424859707429064213156493054604070178326529302927693852725431862420003096049186948750}\cdot t^{25}-\frac{8647169859187524496841450190694794718282651349323635903301106837864656996759304963156493575253}{70813864036657686126916680101843053233931235116731499143573000650053744304807554360016154950}\cdot t^{23}+\frac{7105455054858120694460582401403682776106155649407132381132174774413602322482172728532776561447}{181652955572295803542960179391684353947910559647267758672643784276224822347115030749606658350}\cdot t^{21}-\frac{128997726795833618832830933612385992793095931818014398082426224687301768108279837153874853253}{12975211112306843110211441385120310996279325689090554190903127448301773024793930767829047025}\cdot t^{19}+\frac{1414605352845005303097418513050125800611721223702198362328511927518378495341303882419310283613}{713636611176876371061629276181617104795362912899980480499672009656597516363666192230597586375}\cdot t^{17}-\frac{2829501358222027958826300387644442057148491727084415063002748266391937029029702392406079555859}{9277275945299392823801180590361022362339717867699746246495736125535767712727660498997768622875}\cdot t^{15}+\frac{131328983294263436957632284872111968299707303302319069561884418060268380821720692664365419919}{3710910378119757129520472236144408944935887147079898498598294450214307085091064199599107449150}\cdot t^{13}-\frac{83892974165696271859816006462856870720257826590482749875520514427717662240350060957368049337}{27974555158133553745615867626319390507978226185679234835587142778538622641455714735439425385900}\cdot t^{11}+\frac{1122868247925142510141241482055517730536498355512094199231493074414717140564278015408321205213}{6334965172628243852757193296105600159579432857138815815949779332849064454533289582361782603297900}\cdot t^9-\frac{216149962959760810320950938553984909734052638741752121129992992401554466270998496164923215167}{31674825863141219263785966480528000797897164285694079079748896664245322272666447911808913016489500}\cdot t^7+\frac{694226761665955273563444475277818632967191496377332653387814919366300294548031692069368731}{4524975123305888466255138068646857256842452040813439868535556666320760324666635415972701859498500}\cdot t^5-\frac{374201012999603080636670880284835195421140391551582364651351412689095853886208757957797}{226248756165294423312756903432342862842122602040671993426777833316038016233331770798635092974925}\cdot t^3+\frac{270058309710347928597318330421237828421706565383243608827186807204014019426681182992}{49851420849980127170607453298651817236399895364893829060137488696754139170056152887834850994475}\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.