Rule: Q[14, 27]

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.

• $P_1$:
  $16384\cdot t^{14}-745472\cdot t^{12}+12300288\cdot t^{10}-92252160\cdot t^8+322882560\cdot t^6-484323840\cdot t^4+242161920\cdot t^2-17297280$
• $P_2$:
  $16384\cdot t^{41}-\frac{35422164895437119488}{6845664706949}\cdot t^{39}+\frac{5032015137009021038592}{6845664706949}\cdot t^{37}-\frac{7251108250671053873694720}{116376300018133}\cdot t^{35}+\frac{410251399651016270567700480}{116376300018133}\cdot t^{33}-\frac{16420535635087790272093547520}{116376300018133}\cdot t^{31}+\frac{480843535227422050650561154560}{116376300018133}\cdot t^{29}-\frac{10508305922368603966946805315840}{116376300018133}\cdot t^{27}+\frac{173282923591479923941050217286400}{116376300018133}\cdot t^{25}-\frac{2165831901313725649908936784752000}{116376300018133}\cdot t^{23}+\frac{20499743556687097718431748468136000}{116376300018133}\cdot t^{21}-\frac{146070479833692391047953999264148000}{116376300018133}\cdot t^{19}+\frac{40785789622939818523645743937773000}{6125068422007}\cdot t^{17}-\frac{9317507675025060765439219331797500}{360298142471}\cdot t^{15}+\frac{25857379310690612805160944767613750}{360298142471}\cdot t^{13}-\frac{49565997852881155748574257834173125}{360298142471}\cdot t^{11}+\frac{250171989009815071109581148446093125}{1441192569884}\cdot t^9-\frac{387102673445832242270583356912641875}{2882385139768}\cdot t^7+\frac{328315813068551392733492615368471875}{5764770279536}\cdot t^5-\frac{124941691518537213865102901408690625}{11529540559072}\cdot t^3+\frac{3366972322386398349783666084703125}{5764770279536}\cdot t$

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.