Rule: Q[2, 3, 4, 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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^5-14\cdot t^3+6\cdot t$
• $P_3$:
  $4\cdot t^9-\frac{142}{3}\cdot t^7+\frac{1399}{9}\cdot t^5-\frac{2965}{18}\cdot t^3+\frac{295}{6}\cdot t$
• $P_4$:
  $4\cdot t^{25}-\frac{348014751929152618870273276746}{733464270055645672977186689}\cdot t^{23}+\frac{153951172651106060050334095501747}{6601178430500811056794680201}\cdot t^{21}-\frac{24632777273882457889865235837261211}{39607070583004866340768081206}\cdot t^{19}+\frac{588513253829657275685895530373650731}{59410605874507299511152121809}\cdot t^{17}-\frac{23269302317304109655434464829755368705}{237642423498029198044608487236}\cdot t^{15}+\frac{7383949727826985973919839506480381205}{12186790948616881951005563448}\cdot t^{13}-\frac{56517883464854813075798130791547873535}{24373581897233763902011126896}\cdot t^{11}+\frac{518594847574714663638285824411403957695}{97494327588935055608044507584}\cdot t^9-\frac{149887996532323417856644169086966276615}{21665406130874456801787668352}\cdot t^7+\frac{200323274179145436469215778597849666625}{43330812261748913603575336704}\cdot t^5-\frac{112297857423043112018826691186454021075}{86661624523497827207150673408}\cdot t^3+\frac{2547611754963744844507275162055738625}{28887208174499275735716891136}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Hermite (physicists') type can be downloaded here packed into a single file.