Rule: Q[2, 14, 17]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^{16}-\frac{10827}{1972}\cdot t^{14}+\frac{47593}{5916}\cdot t^{12}-\frac{889889}{147900}\cdot t^{10}+\frac{549549}{226780}\cdot t^8-\frac{1001}{1972}\cdot t^6+\frac{11011}{226780}\cdot t^4-\frac{3861}{2525860}\cdot t^2+\frac{1859}{366249700}$
• $P_3$:
  $\frac{3}{2}\cdot t^{33}-\frac{114468881441127146760608175579567547464511918183071}{9757255117222319715604309309487038439516743069604}\cdot t^{31}+\frac{8502440418161535146429366065647269403359670660412115}{204902357461668714027690495499227807229851604461684}\cdot t^{29}-\frac{15501940216767214599695297356893267888404851079550659}{176639963329024753472146978878644661405044486604900}\cdot t^{27}+\frac{7723073220918610297791300872615552042900971904230658577}{62461988128598200610212484891968590063324429621781100}\cdot t^{25}-\frac{915068439078244660342400865333014712370642759214328887169}{7477949218755776577054638691266479602381200714319633292}\cdot t^{23}+\frac{8554591725531842704113106501138080456122974629016696391379}{97863596297629945638845488959617841752901800652617809604}\cdot t^{21}-\frac{1300758172261905379017879645034687704023244565702203978217785}{28526044862267694642191278989180312848510473648766718111644}\cdot t^{19}+\frac{62664947731309758196303638207815426140059145744959163362154131}{3606518852857012349942852278086295688663483148973889969649284}\cdot t^{17}-\frac{1724991331039972516346566323704274070547584613821431035111031}{360158517453573052730271157729547996268719931429677110512172}\cdot t^{15}+\frac{159255559855618206333796321786981243001514430649344889451087}{170184793961578475465952305300775426808296231334902370901356}\cdot t^{13}-\frac{88356198590769113823193967823991442957679937405062943774009}{705051289269396541216088121960355339634370101244595536591332}\cdot t^{11}+\frac{53895061637627155309481104541593114941981562831221051587175}{4935359024885775788512616853722487377440590708712168756139324}\cdot t^9-\frac{70437268143893283806597004430798505516052067516530138375951}{123383975622144394712815421343062184436014767717804218903483100}\cdot t^7+\frac{44461496854085531801692328723718969557133791922137791442721}{2837831439309321078394754690890430242028339657509497034780111300}\cdot t^5-\frac{702806331815985826305349504519355807574647059963392768951}{3972964015033049509752656567246602338839675520513295848692155820}\cdot t^3+\frac{2735399507074858496256994902651573514051510003942263831}{5806639714279072360407728829052726495227218068442509317319304660}\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.