Rule: Q[3, 8, 22]

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.

• $P_1$:
  $\frac{5}{2}\cdot t^3-\frac{3}{2}\cdot t$
• $P_2$:
  $\frac{5}{2}\cdot t^{11}-\frac{10483}{1482}\cdot t^9+\frac{1617}{221}\cdot t^7-\frac{69993}{20995}\cdot t^5+\frac{68299}{109174}\cdot t^3-\frac{3633}{109174}\cdot t$
• $P_3$:
  $\frac{5}{2}\cdot t^{33}-\frac{182965547209137176300327950593642097998615541222262083}{8620465810351367062145292588452733708607054580974632}\cdot t^{31}+\frac{70714218920211856961976719956759078141982397684969369398029}{862141406159050571252212857063746350931500135697853920952}\cdot t^{29}-\frac{2469274514440322754441274062059002441488651656018888608932667}{12932121092385758568783192855956195263972502035467808814280}\cdot t^{27}+\frac{309792579748697872937297976935186893173519174089252424443009597}{1037347698588484292898912558793701026026357218830228901109912}\cdot t^{25}-\frac{95595999451712089874755822003096504244322713814850703209400535}{288493146944726400983721244161561823806146682159886144095656}\cdot t^{23}+\frac{509983465476805013600927820996142991463351232211164878679451645}{1899558772739951757126580140128725255450861920195613961772696}\cdot t^{21}-\frac{101262051764717097136501133402319500677142376297468091651385}{628784764230371319803568401234268538712632214563261821176}\cdot t^{19}+\frac{140641155195419195601982971045041520177752253703093010975689}{1960328970835863526446419133259778385398206315991345677784}\cdot t^{17}-\frac{1803864125506568236519926809587706555291603375416599327519985}{76452829862598677531410346197131357030530046323662481433576}\cdot t^{15}+\frac{12829017762563360176282180535653937519579534563749179094020355}{2274096919638474388532343042765652325790472162215607535975192}\cdot t^{13}-\frac{2564876503379606640940734717758422058102109845211894195021826465}{2685358601028478487566153696115040681016118320167060868058090184}\cdot t^{11}+\frac{9735650742577295446604888059149359101043623589527025213518588885}{88616833833939790089683071971796342473531904565513008645916976072}\cdot t^9-\frac{11317569499066126197524488992538708607067885321481469794207823}{1406616410062536350629890031298354642437014358182746168982809144}\cdot t^7+\frac{67787595953615616554177240805134776476734469390308838160245}{200945201437505192947127147328336377491002051168963738426115592}\cdot t^5-\frac{28127616753845215740816431958415541582644232215454534333345}{4219849230187609051889670093895063927311043074548238506948427432}\cdot t^3+\frac{55451207415377429119731216936389113652302151072096295475}{1406616410062536350629890031298354642437014358182746168982809144}\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.