Rule: Q[1, 4, 12, 16]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^5-\frac{10}{9}\cdot t^3+\frac{5}{21}\cdot t$
• $P_3$:
  $t^{17}-\frac{8857204}{2038671}\cdot t^{15}+\frac{28927370}{3714291}\cdot t^{13}-\frac{6039926464}{813429729}\cdot t^{11}+\frac{9865688404}{2440289187}\cdot t^9-\frac{11887949788}{9490013505}\cdot t^7+\frac{122410578862}{592447985955}\cdot t^5-\frac{5464102072}{355468791573}\cdot t^3+\frac{39745277}{118489597191}\cdot t$
• $P_4$:
  $t^{33}-\frac{1428479311446303518095268643595248482714012045548045343102146170696165922991476}{174509598479058639024614701840807754485779818263358583504082953996093835373001}\cdot t^{31}+\frac{11613326717107086196174626381367097845814628646970321033889748919739328604317304554}{381303472676743126268783123522164943551428902905438504956421254481465030290007185}\cdot t^{29}-\frac{56461337206919128278965789691690898092953686350963236991535366600465326829828994024}{828348923401200584652873682134358325646207616656642269388087552839044720974843195}\cdot t^{27}+\frac{740247348685601663731846893409028653487460676093662982978938681450405815928539964599786}{7234755899674327948432690693778215386808416997162447441768746787151330327482650210225}\cdot t^{25}-\frac{5658587524358678395650130908499974807323524131740407271203357513452607899116327624485532}{52023460115504321278422148158029813412219293914980429758195573050992796847159857050141}\cdot t^{23}+\frac{312357365649819558147991934710001853775724794773863429774499567283890372201757141470876907342646}{3706630347990424783499899305392332432018340017834672927431209341721238072729302479935714888375}\cdot t^{21}-\frac{25516415992176432251232250476681864578976325459863535368247671184059717979892396863244649729539264}{528989102520347765530914200869562871369474525402405464929111161768502404950939025350825596212375}\cdot t^{19}+\frac{120071013627839163944233019191567002390867867409654229268485746242418277084563666677615209070871510684}{5868855677146142486057318893278921340543599083273687367354315123420603392191220623622488502820399375}\cdot t^{17}-\frac{112507634138322303938937994115200462479411407480467482680995661291358742707353735244746460398746005308}{17606567031438427458171956679836764021630797249821062102062945370261810176573661870867465508461198125}\cdot t^{15}+\frac{1698557692598651179240619667989457897593571727712322439950290271967140581811587180192791698871560106}{1173771135429228497211463778655784268108719816654737473470863024684120678438244124724497700564079875}\cdot t^{13}-\frac{605808688181976290993438291076514301252090654459137942266478527355524571855335240367653661015173128}{2618412532880586647625573044693672598088682667922106671588848285833807667285313816693110255104485875}\cdot t^{11}+\frac{1770913225564935446929136823050612465006942288459316134531046457476085621407854778910417607455578806}{70697138387775839485890472206729160148394432033896880132898903717512807016703473050713976887821118625}\cdot t^9-\frac{2365802670368718560734908731096415729199302173190260938135596909275340625999804092722214792441619756}{1374666579762307990003425848464178113996558400659106002584145350062749025324789753763882883929855084375}\cdot t^7+\frac{304914911584466640366633498908244740939379377306768335772948893063671269082945006813845641396604546}{4516761619219011967154113502096585231702977602165634008490763293063318226067166333795615190055238134375}\cdot t^5-\frac{3385326807350847971252377460872248691973800366503798409361862452311910214730555501415376582258736}{2710056971531407180292468101257951139021786561299380405094457975837990935640299800277369114033142880625}\cdot t^3+\frac{68477498187654801489678671327112551668314595682597515383298554420922655179035898381972306633}{9735504340914489776055377939856508156818669817486902570768519860261264469118112347375687874197336875}\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.