Rule: Q[2, 3, 50]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^5-\frac{25}{14}\cdot t^3+\frac{3}{7}\cdot t$
• $P_3$:
  $\frac{3}{2}\cdot t^{55}-\frac{9090227048386963652162534097681486631773554373}{448257390045035786868507593273060696264332784}\cdot t^{53}+\frac{197180133391548479408781467627085800181146847815}{1522104763999077562004053256278854452150316816}\cdot t^{51}-\frac{93269699168876544311202978731565490286127199889975}{179354678024557972722810942031525016278378998152}\cdot t^{49}+\frac{56561483503101466874426300329255327632266112517925}{38433145290976708440602344721041074916795499604}\cdot t^{47}-\frac{69841796680509618543333371113193880718285071640192885}{22368090559348444312430564627645905601574980769528}\cdot t^{45}+\frac{243481368527505877173252493611624992848853983928322655}{47221524514180049104020080880585800714436070513448}\cdot t^{43}-\frac{2485543858983934179284575274864982558202019539223375525}{365966814984895380556155626824539955536879546479222}\cdot t^{41}+\frac{207104611510620379986946402779148111275556619860940594075}{28545411568821839683380138892314116531876604625379316}\cdot t^{39}-\frac{87179975846040803136984039658798301642917388473571287925}{13714124856276079523999095068372234123276749320695056}\cdot t^{37}+\frac{1830501338676884612723638200138999104686087062171355146285}{397709620832006306195973756982794789575025730300156624}\cdot t^{35}-\frac{1650170255607800275795391972627323980624298046947521000745}{596564431248009459293960635474192184362538595450234936}\cdot t^{33}+\frac{5705492878815885003894770478929701225318045448019991043975}{4126237316132065426783227728696495941840891951864124974}\cdot t^{31}-\frac{142476406104269180967313884307030152665468502526179977075}{247849627442860437203886871356630457018251574416755004}\cdot t^{29}+\frac{151446814935213711009059783339085835583983323913756778339675}{763624702151453007025175450649778438073233100778022167324}\cdot t^{27}-\frac{30753849623015660632451613621514120241895390933017619940}{543892237999610403864085078810383502901163177192323481}\cdot t^{25}+\frac{7199606400069500379471429541568144072801137605382220315}{543892237999610403864085078810383502901163177192323481}\cdot t^{23}-\frac{4806599451330427530532872039625335861899815650023572748575}{1905798401950634855139754116151583794165675772881901477424}\cdot t^{21}+\frac{17433476919672130176038404033391784707743716290585312960575}{45103895512831691571640847415587483128587659958205001632368}\cdot t^{19}-\frac{352700566892616517489483840997972239850325429081875563425}{7517315918805281928606807902597913854764609993034166938728}\cdot t^{17}+\frac{1415226624084538403528360174552495980778811420654223355}{320077778494533611280179717925896204944432977390171067932}\cdot t^{15}-\frac{6188532781703003208916213598614642827862041782275639376155}{19642746495838201679449589049488348902499925911798278210896264}\cdot t^{13}+\frac{940037885818371479987748538581310882252710300968612275}{57379006316956772189239305889449899423076706655691172962696}\cdot t^{11}-\frac{122747659548575989172453289178506906053728898648703206425}{207382073581061013884958161310944298989854987030331821880424018}\cdot t^9+\frac{8068270932683336213991503043351648670134187419216025}{583353230889060517257266276542740644134613184332860258454076}\cdot t^7-\frac{38603406690060475960424462667012127905050396107794055243}{206644715097217241391144976737394274815668835965335086513738065936}\cdot t^5+\frac{740121915155245651575879296346934116465425314980125117}{619934145291651724173434930212182824447006507896005259541214197808}\cdot t^3-\frac{3063290443331825233343003101185884650760390031166145}{1343190648131912069042442348793062786301847433774678062339297428584}\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.