Rule: Q[6, 45]

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.

• $P_1$:
  $\frac{231}{16}\cdot t^6-\frac{315}{16}\cdot t^4+\frac{105}{16}\cdot t^2-\frac{5}{16}$
• $P_2$:
  $\frac{231}{16}\cdot t^{51}-\frac{46213783449392057742359915638407749000631}{257843312538486074765825846902074882320}\cdot t^{49}+\frac{45451657376438440085350026371598775756108571697}{43422747656325093636125816312161175744305400}\cdot t^{47}-\frac{3438898256886311888821885329343292723574789456629}{899551243383612101068387072118384098806223480}\cdot t^{45}+\frac{3037598560226704918263427365333785583429668728243194}{310232735061923223355959991496827716075796322665}\cdot t^{43}-\frac{11597920749032162072472509367864986821745376762091473}{620465470123846446711919982993655432151592645330}\cdot t^{41}+\frac{1670588113592226419087537764834653427411808779581237}{60533216597448433825553169072551749478204160520}\cdot t^{39}-\frac{3282245329375078458853041351854003101380127907542641}{101705606833769635779775567470076826046375411400}\cdot t^{37}+\frac{35823315484067690434858734866183866260574413227228823}{1179785039271727775045396582652891182137954772240}\cdot t^{35}-\frac{82203372564382027580863791639567234492095212410598733}{3539355117815183325136189747958673546413864316720}\cdot t^{33}+\frac{3804938674508657895957124509697339301480487722361349}{261806230624905882664568342779714616260950637660}\cdot t^{31}-\frac{84141622131551089885104221448528337760888915791978481}{11274558641427398495393507664868355248657067783100}\cdot t^{29}+\frac{669614444520818247104099641587829574197430789021339107}{212855891592465540559584325741911189608267055560250}\cdot t^{27}-\frac{5611721154419065370617901183641094847101102888292759}{5166758394210274659736918676128442551175029382830}\cdot t^{25}+\frac{3158521846857416437863030405661539140343101158319307}{10333516788420549319473837352256885102350058765660}\cdot t^{23}-\frac{48177122356547920476436270730476417357962639501798389}{692345624824176804404747102601211301857453937299220}\cdot t^{21}+\frac{1186730810831687689788430780516093329317658498628716525}{93605128476228703955521808271683768011127772322854544}\cdot t^{19}-\frac{4263225706291604840247339715302103630732045683747998517}{2340128211905717598888045206792094200278194308071363600}\cdot t^{17}+\frac{2890366992995243085769588108076595298815978188156357379}{14274782092624877353217075761431774621696985279235317960}\cdot t^{15}-\frac{14282096761981359295370915566514997527212500350786841957}{842212143464867763839807469924474702680122131474883759640}\cdot t^{13}+\frac{16729479387586449442670946269112841990936824136535051}{16196387374324380073842451344701436590002348682209303070}\cdot t^{11}-\frac{1057943854306752764312067355392351797712642479149651}{24294581061486570110763677017052154885003523023313954605}\cdot t^9+\frac{385518340093380775248152139198151811278312552399643397}{326195241718893014687186970082286932922647302459695363829800}\cdot t^7-\frac{15215068324279211126308572479789314790791257614619}{825810738528843075157435367296928944107967854328342693240}\cdot t^5+\frac{123010148216652227052118129258858586530480662961243}{913346676812900441124123516230403412183412446887147018723440}\cdot t^3-\frac{265160031225391346998606358638753155361214339043}{913346676812900441124123516230403412183412446887147018723440}\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.