Rule: Q[3, 10, 14]

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.

• $P_1$:
  $\frac{5}{2}\cdot t^3-\frac{3}{2}\cdot t$
• $P_2$:
  $\frac{5}{2}\cdot t^{13}-\frac{124943}{17112}\cdot t^{11}+\frac{2882165}{359352}\cdot t^9-\frac{1552265}{379316}\cdot t^7+\frac{52195}{54188}\cdot t^5-\frac{488345}{5527176}\cdot t^3+\frac{3421}{1842392}\cdot t$
• $P_3$:
  $\frac{5}{2}\cdot t^{27}-\frac{6014454661153989176140823607177861773681}{379434848926985219727647194405121838204}\cdot t^{25}+\frac{9735694977147497444462482798002939641194025}{219566299245748780482398509829097170374048}\cdot t^{23}-\frac{10225924295888781146489515232345610210325228075}{142021210168652374227680114379455591463248352}\cdot t^{21}+\frac{508182124905276163414707821801182562300683325}{6762914769935827344175243541878837688726112}\cdot t^{19}-\frac{915609317114203214426598475076870368034794561625}{17372504272434627641429532186762127951245018336}\cdot t^{17}+\frac{44383227353608589421261374801062353686517188461775}{1758199623571986873945853536901425949418650238064}\cdot t^{15}-\frac{139765158779705879428777582719059454467575949211625}{16995929694529206448143250856713784177713618967952}\cdot t^{13}+\frac{272540837187498941326160708484034468354741171847375}{152963367250762858033289257710424057599422570711568}\cdot t^{11}-\frac{2473544338926079907127173548394859572601774209905}{10069688753185015732598979347708166801215905908912}\cdot t^9+\frac{29790910334857621381699179510764405637343060016785}{1492551644083201220809670938871410501424668720276512}\cdot t^7-\frac{59349905617437372548514211668095053166542769413}{71073887813485772419508139946257642924984224775072}\cdot t^5+\frac{166671358100895253451203707387317733970035666445}{12153634816106067083735891930810056940172302436537312}\cdot t^3-\frac{2742604298999482320458206389364891463962269535}{68870597291267713474503387607923655994309713807044768}\cdot t$

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.