Rule: Q[2, 6, 32]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^8-\frac{161}{52}\cdot t^6+\frac{105}{52}\cdot t^4-\frac{245}{572}\cdot t^2+\frac{25}{1716}$
• $P_3$:
  $\frac{3}{2}\cdot t^{40}-\frac{32753391346002444711417368697663296609362685370786172381}{2114350332602141585512026716786491322371454032005135076}\cdot t^{38}+\frac{470015681484128861739235836489762190758001310596778149583}{6343050997806424756536080150359473967114362096015405228}\cdot t^{36}-\frac{5964197815312781979905770036030854259260375827831491531426415}{27381138857245248124035819129058889266327811350756785682068}\cdot t^{34}+\frac{92416158490809897518930872562208687544238575358562492473004845}{209922064572213568950941279989451484375179887022468690229188}\cdot t^{32}-\frac{1211839545719891642216270324715682992066467784157883230917177113}{1868762727006988184465444655558269192426873124689150622801141}\cdot t^{30}+\frac{9299187918329782352944776376114658552310586123286569008335863577}{12915635990102484841404033752454441758497059083442750363497541}\cdot t^{28}-\frac{52046735513167368225281220944656917353142072416127147698266914177}{84669169268449622849204221266090229305702942880346919049594991}\cdot t^{26}+\frac{18603509486637788584655181557793512650439614454994935473204626350}{45591091144549796918802272989433200395378507704802187180551149}\cdot t^{24}-\frac{9225989212073178741700484195591484871926162681539660820057355075}{43608869790438936183202174163805669943405529108941222520527186}\cdot t^{22}+\frac{2569216589891272150926082197135296111024925532678915190454935235}{30016494790821605424801496502359746844162247308751750566077154}\cdot t^{20}-\frac{806225269402030912496269305853212169823879012908733265962524565}{30016494790821605424801496502359746844162247308751750566077154}\cdot t^{18}+\frac{179349349533590738989043110670980852770027570880039085682907795}{27751098957552050298401383558785426327621700342053505240335482}\cdot t^{16}-\frac{247584688501248643810879537063088038470579449228953128860775}{211383766132546517076066876777181315803959488089801060324487}\cdot t^{14}+\frac{49091910020260100864848409871107143738969816652319949912600325}{315173195303626856960415713274777341863703596741893380943810117}\cdot t^{12}-\frac{1388693389518931591834867578914044115599359252372471085787391995}{94867131786391683945085129695707979900974782619309907664086845217}\cdot t^{10}+\frac{2115075181255436346739256154400251170225609825134783087729105005}{2299483810721720439775837043064519210933061712042895497719438374002}\cdot t^8-\frac{1235448431146257475962024881279002321624327833978387791023144015}{34820754848071766659462675223548433765557791639506703251180066806316}\cdot t^6+\frac{329356703684638554031405072731550161847982145526033597729903675}{452669813024932966573014777906129638952251291313587142265340868482108}\cdot t^4-\frac{18874565734151527689487616699107620380174468109113224722828675}{3168688691174530766011103445342907472665759039195109995857386079374756}\cdot t^2+\frac{40621451744539340969902545135889519476673752824180248376625}{4979367943274262632303162556967426028474764204449458564918749553303188}$

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.