Rule: Q[2, 4, 42]

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^{48}-\frac{57390053754844371717624076504072556945141774987}{3198085752699181907101131185999209621103205010}\cdot t^{46}+\frac{13060591299648405562811893224808375937808588369501}{129842281559586785428305926151567910616790123406}\cdot t^{44}-\frac{3874072088471280174330858915728516651760293618229297}{11036593932564876761406003722883272402427160489510}\cdot t^{42}+\frac{22369269292007072278830258404007524098160240739032175}{26172494182939564891334237399980331697184409160838}\cdot t^{40}-\frac{3105084983255671431403194965383903048716757535001923}{2013268783303043453179556723075410130552646858526}\cdot t^{38}+\frac{15306221741985291279893739023857463693513257473123755993}{7157170524642319476053324150533083014114659582059930}\cdot t^{36}-\frac{158923926389683740590987380109112876822289675446670289}{68163528806117328343364991909838885848711043638666}\cdot t^{34}+\frac{237190915527739611570347221793479657659583655097554971}{116947230794809141765577192002174559054161104282025}\cdot t^{32}-\frac{10187918655597146763526210766519885024133931024643381155}{7171204192337696573065193413573343961201158914573773}\cdot t^{30}+\frac{212052563338745563055216679519777182492828467135488439279}{263356291891022305183256240877779700644111525655898905}\cdot t^{28}-\frac{7728358762830798207037237788733643932954889411450946501}{20901293007223992474861606418871404813024724258404675}\cdot t^{26}+\frac{7692486581122165295932799632023971849652967770173091413}{56015465259360299832629105202575364898906261012524529}\cdot t^{24}-\frac{11497469652485552469894338389802504556176927175245369777}{280077326296801499163145526012876824494531305062622645}\cdot t^{22}+\frac{1019168154051609793303304771356961722885399997021804895}{104028721195954842546311195376211391955111627594688411}\cdot t^{20}-\frac{245836646871419287643623874996073533307495420030194611295}{133260791852018153301824641276926793094497994948795854491}\cdot t^{18}+\frac{49470753235129260597806450227132597573102334523428781959623}{183455690116278324378845256157902551826758906379508959682610}\cdot t^{16}-\frac{1098272181589968945102209486457286935738729898676845448571}{36691138023255664875769051231580510365351781275901791936522}\cdot t^{14}+\frac{4936891058647218879108067901685837783998303443030445757}{2015996594684377190976321496240687382711636333840757798710}\cdot t^{12}-\frac{171388468950283028002598100592259177998620695344583995}{1209597956810626314585792897744412429626981800304454679226}\cdot t^{10}+\frac{37464950321375838871829088503391702734548974869279439}{6854388421926882449319493087218337101219563535058576515614}\cdot t^8-\frac{233539666222920053958984261589324165465399440498580991}{1816412931810623849069665668112859331823184336790522776637710}\cdot t^6+\frac{4043715836404046766821842447902009727877002578251573}{2542978104534873388697531935358003064552458071506731887292794}\cdot t^4-\frac{687498118402237793206870810621680518203286555804703}{89004233658720568604413617737530107259336032502735616055247790}\cdot t^2+\frac{163781501139515446201574409760327516578673067380}{26701270097616170581324085321259032177800809750820684816574337}$

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.