Rule: Q[1, 2, 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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{5}\cdot t$
• $P_3$:
  $t^{11}-\frac{10483}{3705}\cdot t^9+\frac{3234}{1105}\cdot t^7-\frac{139986}{104975}\cdot t^5+\frac{68299}{272935}\cdot t^3-\frac{3633}{272935}\cdot t$
• $P_4$:
  $t^{33}-\frac{182965547209137176300327950593642097998615541222262083}{21551164525878417655363231471131834271517636452436580}\cdot t^{31}+\frac{70714218920211856961976719956759078141982397684969369398029}{2155353515397626428130532142659365877328750339244634802380}\cdot t^{29}-\frac{2469274514440322754441274062059002441488651656018888608932667}{32330302730964396421957982139890488159931255088669522035700}\cdot t^{27}+\frac{309792579748697872937297976935186893173519174089252424443009597}{2593369246471210732247281396984252565065893047075572252774780}\cdot t^{25}-\frac{19119199890342417974951164400619300848864542762970140641880107}{144246573472363200491860622080780911903073341079943072047828}\cdot t^{23}+\frac{101996693095361002720185564199228598292670246442232975735890329}{949779386369975878563290070064362627725430960097806980886348}\cdot t^{21}-\frac{20252410352943419427300226680463900135428475259493618330277}{314392382115185659901784200617134269356316107281630910588}\cdot t^{19}+\frac{140641155195419195601982971045041520177752253703093010975689}{4900822427089658816116047833149445963495515789978364194460}\cdot t^{17}-\frac{360772825101313647303985361917541311058320675083319865503997}{38226414931299338765705173098565678515265023161831240716788}\cdot t^{15}+\frac{2565803552512672035256436107130787503915906912749835818804071}{1137048459819237194266171521382826162895236081107803767987596}\cdot t^{13}-\frac{512975300675921328188146943551684411620421969042378839004365293}{1342679300514239243783076848057520340508059160083530434029045092}\cdot t^{11}+\frac{1947130148515459089320977611829871820208724717905405042703717777}{44308416916969895044841535985898171236765952282756504322958488036}\cdot t^9-\frac{11317569499066126197524488992538708607067885321481469794207823}{3516541025156340876574725078245886606092535895456865422457022860}\cdot t^7+\frac{13557519190723123310835448161026955295346893878061767632049}{100472600718752596473563573664168188745501025584481869213057796}\cdot t^5-\frac{5625523350769043148163286391683108316528846443090906866669}{2109924615093804525944835046947531963655521537274119253474213716}\cdot t^3+\frac{11090241483075485823946243387277822730460430214419259095}{703308205031268175314945015649177321218507179091373084491404572}\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.