Rule: Q[1, 12, 28]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{13}-\frac{78}{25}\cdot t^{11}+\frac{429}{115}\cdot t^9-\frac{1716}{805}\cdot t^7+\frac{1287}{2185}\cdot t^5-\frac{2574}{37145}\cdot t^3+\frac{429}{185725}\cdot t$
• $P_3$:
  $t^{41}-\frac{6480388755146046950027557498984984214987525794}{625410696539947778170612064609927135420169325}\cdot t^{39}+\frac{19604163731221747603332023939905435640703463266576}{393883656680859110691851478291332109887622640885}\cdot t^{37}-\frac{46631687653193011739917692464603526763747660742014902}{317076343628091584106940440024522348459536225912425}\cdot t^{35}+\frac{463432637994191207597638153521759232828701910901446787}{1549144421725818882351051864119809188188019846600705}\cdot t^{33}-\frac{237843370507014538301637372592382911179753029762880147352}{535487588443224726999346927697414042716992193641643695}\cdot t^{31}+\frac{3382778297283991978176633700697562399845481558496179880150928}{6792660059402305661986715777841697131865045976344250271075}\cdot t^{29}-\frac{584647558250994347036341449659725097347088780327190346720136}{1358532011880461132397343155568339426373009195268850054215}\cdot t^{27}+\frac{12474859861475566694455445907716949849231963889839998219854398}{43020180376214602525915866592997415168478624516846918383475}\cdot t^{25}-\frac{11458807136922333912864419209113371740076843743161034465596}{74817705002112352218984115813908548119093260029298988493}\cdot t^{23}+\frac{564557769514222642961787833495732837060702635091639352902768}{8903306895251369914059109781855117226172097943486579630667}\cdot t^{21}-\frac{6855365356890830548585398615302542746313716458979052745244}{334710785535765786242823676009590873164364584341600737995}\cdot t^{19}+\frac{945968559167643288159027461330192422990302372772451987622}{185075375531541081804855444381773776926178064283002761009}\cdot t^{17}-\frac{142791293559429902206265850614786384345715300673594124851352}{147134923547575160034860078283510152656311561104987195002155}\cdot t^{15}+\frac{404748488671076368602691930336002355447499307865513195485712}{2952507465854674878032858904222437063303318659506743046376577}\cdot t^{13}-\frac{41194486601592997182518206272041659197997278433275250591256}{2952507465854674878032858904222437063303318659506743046376577}\cdot t^{11}+\frac{306885471403707685175731052145198517468574830417370591799}{314096538920710093407750947257706070564182836117738621954955}\cdot t^9-\frac{908184537307218867511056607844543353260108249316201235094}{20667552260982724146230012329557059443123230616547201324636039}\cdot t^7+\frac{16787811237141342776279174389547353302774586022683565856}{14762537329273374390164294521112185316516593297533715231882885}\cdot t^5-\frac{41021645768495919667335313720640341902556755070033046}{2952507465854674878032858904222437063303318659506743046376577}\cdot t^3+\frac{149805712472470601432980486941214055728129912528551}{2952507465854674878032858904222437063303318659506743046376577}\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.