Rule: Q[2, 6, 24]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^8-\frac{161}{52}\cdot t^6+\frac{105}{52}\cdot t^4-\frac{245}{572}\cdot t^2+\frac{25}{1716}$
• $P_3$:
  $\frac{3}{2}\cdot t^{32}-\frac{522927807673413173290026387860349494633}{45144571433576497187084555308698392500}\cdot t^{30}+\frac{31254395641845655327497769112084103704388303}{772829918371396055345700502329607781207500}\cdot t^{28}-\frac{248887202745943447608715036153399038464667449}{2949371321131654333666244774196666430322500}\cdot t^{26}+\frac{1094517873478634872452513732861149006876118961}{9338163352136837874900202685071906944005700}\cdot t^{24}-\frac{315293444347565685753325200199905742690420249}{2760337594656801132832135384895469348228100}\cdot t^{22}+\frac{761891155894654724421954354294526078354925693}{9499863150442237664941764636328563341304500}\cdot t^{20}-\frac{7935679907628761398036905908716561976249255521}{193497212590586630333287521803113369109728500}\cdot t^{18}+\frac{5538585138623138508087201726964951149290516899}{362965359565348777161134109526101548591451500}\cdot t^{16}-\frac{5592595212967484128872592725667275878310277}{1369680602133391611928807960475854900345100}\cdot t^{14}+\frac{200703608310465162889346139243814229347123}{261439634740947498555438734352534128637300}\cdot t^{12}-\frac{1311072487059758860835967065571540025649855309}{13429718303917904754961962052465757297883705500}\cdot t^{10}+\frac{106244115733166372699393649937552662539914901}{13429718303917904754961962052465757297883705500}\cdot t^8-\frac{2138485466534552936103077105033541520594249}{5755593558821959180697983736771038841950159500}\cdot t^6+\frac{472203675821328082297031287105959562041697}{54869991927436010855987444957217236959924853900}\cdot t^4-\frac{585442094050124046078444636210021259021}{8172126457277703744508768397883418270627105900}\cdot t^2+\frac{10532874792536692997302225447045981231}{122005040873945953550372083493106562181479969260}$

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.