Rule: Q[1, 14, 16]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{15}-\frac{105}{29}\cdot t^{13}+\frac{455}{87}\cdot t^{11}-\frac{1001}{261}\cdot t^9+\frac{1001}{667}\cdot t^7-\frac{1001}{3335}\cdot t^5+\frac{1001}{38019}\cdot t^3-\frac{143}{215441}\cdot t$
• $P_3$:
  $t^{31}-\frac{7409}{957}\cdot t^{29}+\frac{1031711}{38115}\cdot t^{27}-\frac{2629168559}{46538415}\cdot t^{25}+\frac{1259755805600003}{16071808928175}\cdot t^{23}-\frac{1946925760686509}{25552476474525}\cdot t^{21}+\frac{1758744880054675345187599}{33009617047974567375375}\cdot t^{19}-\frac{26400803264837576523071393}{974652377048091173557125}\cdot t^{17}+\frac{404604720536578716756978687271}{40459826808513128331478288125}\cdot t^{15}-\frac{1020667792925350833700218539}{385331683890601222204555125}\cdot t^{13}+\frac{422409064753545587151875659}{859586064063648880302469125}\cdot t^{11}-\frac{129468337008028564289678927}{2109893066338047251651515125}\cdot t^9+\frac{1134512772469530672045523}{234432562926449694627946125}\cdot t^7-\frac{29242025660691500133609521}{134798723682708574411069021875}\cdot t^5+\frac{368242414624854591770119}{80879234209625144646641413125}\cdot t^3-\frac{101959200754203074874413}{3585646049960048079334435981875}\cdot t$

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.