Rule: Q[2, 17, 20]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^{19}-\frac{746491}{110950}\cdot t^{17}+\frac{2101438}{166425}\cdot t^{15}-\frac{6950314}{540485}\cdot t^{13}+\frac{120809429}{15674065}\cdot t^{11}-\frac{684437}{248211}\cdot t^9+\frac{60910694}{106868625}\cdot t^7-\frac{153288694}{2457978375}\cdot t^5+\frac{61922653}{20647018350}\cdot t^3-\frac{276029}{6882339450}\cdot t$
• $P_3$:
  $\frac{3}{2}\cdot t^{39}-\frac{65822967321607937893021911009189595903753315170710917011696513958504519}{4633173321540989010239063358278102538075518218024572741092259737356050}\cdot t^{37}+\frac{35320036367130670499997349372840131824851360521327049525178887705546161679}{569880318549541648259404793068206612183288740817022447154347947694794150}\cdot t^{35}-\frac{118279847937202673476396291497827179523680570627325691368807075007948239077181}{716241866647879644722370212636495447523733954851428583653503196318465710410}\cdot t^{33}+\frac{3876902667696297838022273069575368325963856015841361189945754083372134266703446}{12903205749156498448104517921587774047056358671490130090363868188222056510265}\cdot t^{31}-\frac{113187805319753967608795194349123423669676508621626331466346368359281754229266}{286286705056029312538589618716581611429574598376098873759450104569521631463}\cdot t^{29}+\frac{5305520267551881860034818138685690958969736132363774461792471739861927113092816926618}{13647113236807930690209963929666690942678805716578413355469882681101750040160019125}\cdot t^{27}-\frac{23687190258203757537522616619865677547157191656089757097985165090373379259162508668358}{81377230782447290411992747876901379324862508161819427786320411542865990980213447375}\cdot t^{25}+\frac{8296264155339676416150737192363523295566698799898352225044289588663095043213112873837353}{49513162297272229378272867518221875236419344465977412642308791199141383552001069920845}\cdot t^{23}-\frac{20650823889996757908948712225294825083412621639725086697268992062905416457922136324875131}{277704258102092069121617387384809648065134584178742879602514524551706020791658174773435}\cdot t^{21}+\frac{1089626305666082919814739143287552343887502274484071170815850277497396331634383066354226611}{42956503695783882468903463433933555533971899699365733619930182095043690641994548114987953}\cdot t^{19}-\frac{49554242068496087416435635824713602941091517754009677951430351629200446778277673629323114593}{7517388146762179432058106100938372218445082447389003383487781866632645862349045920122891775}\cdot t^{17}+\frac{1705427102580346665675759775291827825178082861167860906763902336819590684037490700619965654}{1326597908252149311539665782518536273843249843656882950027255623523408093355713985904039725}\cdot t^{15}-\frac{16265400660935600281872787906422773928368304108841628115257138430853696798440337698263794}{88439860550143287435977718834569084922883322910458863335150374901560539557047599060269315}\cdot t^{13}+\frac{229989400348362417397899773458112951382675757433239362204145567651646671390637843253574}{12314410962678179263237403888357720685464766481203132869451318024267923229462323919784335}\cdot t^{11}-\frac{44340998383219707640297175195744717873659523907544280846008074698355703463569074420747566}{34544609530885968072492896976782684570878225928825232018709736436549546750982792192941194439}\cdot t^9+\frac{9982598703727009371899144158477012783832666818846401729869051977834003001935141854652423}{179532916916790873495034769234175242393453145508231492570355261050167895300806626092346709450}\cdot t^7-\frac{153988806270284725465170747428524493683498611123277281854003137751593689070812463852429}{113582049477969736292777098903253724779531581852146454483285981480718464373979702221688734550}\cdot t^5+\frac{7253066459715012358328570183150708984825301732473909136966890761572874499750280072479}{477044607807472892429663815393665644074032643779015108829801122219017550370714749331092685110}\cdot t^3-\frac{181002163623370687013291906464961455131166248185749094250946784198009571022787358911}{3657341993190625508627422584684769937900916935639115834361808603679134552842146411538377252510}\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.