Rule: Q[2, 9, 18]

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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^{11}-\frac{1238}{7}\cdot t^9+\frac{15354}{7}\cdot t^7-9783\cdot t^5+\frac{59445}{4}\cdot t^3-\frac{41985}{8}\cdot t$
• $P_3$:
  $4\cdot t^{29}-\frac{2043513178851919911531877162}{2850224919301609318221683}\cdot t^{27}+\frac{22525821539178627681014146092}{407174988471658474031669}\cdot t^{25}-\frac{75810174031233247115369962468215}{31352474112317702500438513}\cdot t^{23}+\frac{41592892484187154753690246367848443}{627049482246354050008770260}\cdot t^{21}-\frac{214420888020936329369418966738563943}{179156994927529728573934360}\cdot t^{19}+\frac{2595908330326416111636630062278681479}{179156994927529728573934360}\cdot t^{17}-\frac{21150010596697885735279728724273703031}{179156994927529728573934360}\cdot t^{15}+\frac{183605529121517298860656872021148360473}{286651191884047565718294976}\cdot t^{13}-\frac{117761403601833167872513315908748990197}{52118398524372284676053632}\cdot t^{11}+\frac{64843389777761921338367830165649282337}{13029599631093071169013408}\cdot t^9-\frac{668590035205608249624347295527423570043}{104236797048744569352107264}\cdot t^7+\frac{1811229591549404416703024650011408191493}{416947188194978277408429056}\cdot t^5-\frac{24566974753529111223411036510323895045}{19392892474185036158531584}\cdot t^3+\frac{83050422651051956810709965526697173765}{833894376389956554816858112}\cdot t$

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.