Rule: Q[2, 4, 6, 22]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^6-\frac{25}{14}\cdot t^4+\frac{45}{98}\cdot t^2-\frac{1}{98}$
• $P_3$:
  $\frac{3}{2}\cdot t^{12}-\frac{1595}{364}\cdot t^{10}+\frac{318813}{66248}\cdot t^8-\frac{10310751}{4183088}\cdot t^6+\frac{2471775}{4183088}\cdot t^4-\frac{33827}{597584}\cdot t^2+\frac{31245}{29281616}$
• $P_4$:
  $\frac{3}{2}\cdot t^{34}-\frac{21259245294933518877534799704140846651572732824530222048069863340719247502056757129186773}{1667895996219657521686226478874808654216690924475431876040686551934279460764502885941572}\cdot t^{32}+\frac{2386262681858769790540038674695540292685342264252789312686924635430737847905044264787117112593}{48265574338604449362556021845679212835722601972470047628865387439874179035603184513377210536}\cdot t^{30}-\frac{7420062853499545743310677006754539568953098344612507804584494628976736544863125122429105112097623}{64000151572989499854749284967370636220168170215495283155875503745273161401209822664738181170736}\cdot t^{28}+\frac{6524545050924956715371519788005715061393328089520217514307060524114768058944150640081175201256751}{35555639762771944363749602759650353455648983453052935086597502080707311889561012591521211761520}\cdot t^{26}-\frac{4662450006919189797788708749002273514659795060423665619069142074434977371845631981325090252936545}{22495779772984557107064652515240319782516376069335414699020342662601356945510717581943228210654}\cdot t^{24}+\frac{92981256151935782090794830806531270573714963864975423333607343814613270080460064210089788571534169}{539898714551629370569551660365767674780393025664049952776488223902432566692257221966637477055696}\cdot t^{22}-\frac{671931985934414365539150485245430765829343625269621039944169577470175620032798910883116768466920}{6281289157391791919505065312696972406806520590788459948427758016180898367902343220932200084793}\cdot t^{20}+\frac{3014095534894833976276902641011697998471116867489276538931865184419775478850814166094169819305}{60324505713246501027659690878242231998141854413334549324636331487931797050682768028160384968}\cdot t^{18}-\frac{9419244759701058947632340323359167189089331346737038483514493955948900999002878944164398998555763}{537973941950732296164669123252164224959429057658117510877106804209375766097988925275134313144624}\cdot t^{16}+\frac{22673736486631398638196366267940578585724960234904780914260804459734095661862000439536944138633775}{4976258963044273739523189390082519080874718783337586975613237938936725836406397558794992396587772}\cdot t^{14}-\frac{7746870127936361125171368623126516832165212768520452433996808779752249234567836608820482144473561}{8968202966365504321778055604104759662235756928212794109896384856984868540336804391674491791652688}\cdot t^{12}+\frac{239623229476076817645418294768104745255854225811717570856590528367852444725865960402869647948920455}{2071654885230431498330730844548199481976459850417155439386064901963504632817801814476807603871770928}\cdot t^{10}-\frac{76567030021443194324315526411012294744278001427728695801468271898468978086628140386806002594975}{7346293919256849284860747675702835042469715781621118579383208872211009336233339767648253914438904}\cdot t^8+\frac{57684152159317487512280958920723262060318707707375175962296589820475625798423246429100038453587}{98650232630020547539558611645152356284593326210340735208860233426833553943704848308419409708179568}\cdot t^6-\frac{7922169264628429005922569118953020089803675534320555223041526417041447928020159195874545833265}{443926046835092463928013752403185603280669967946533308439871050420750992746671817387887343686808056}\cdot t^4+\frac{1892100840716277323667271623563060594497192043517751809056950904148335458269569872252453523419}{8416097971248627961968594055977060395529368142319693972505888664226737570822319871312030890729069395}\cdot t^2-\frac{4452128624755336138660113833184709761874980992710244011570675114237805640552076338002406109}{8977171169331869826099833659708864421897992685141006904006281241841853408877141196066166283444340688}$

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.