Rule: Q[18, 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.

• $P_1$:
  $262144\cdot t^{18}-20054016\cdot t^{16}+601620480\cdot t^{14}-9124577280\cdot t^{12}+75277762560\cdot t^{10}-338749931520\cdot t^8+790416506880\cdot t^6-846874828800\cdot t^4+317578060800\cdot t^2-17643225600$
• $P_2$:
  $262144\cdot t^{45}-\frac{225459593443788744497457659904}{2416372265418801343709}\cdot t^{43}+\frac{36295556663166650839325520691200}{2416372265418801343709}\cdot t^{41}-\frac{3507747625061994496659862381461504}{2416372265418801343709}\cdot t^{39}+\frac{227822982293057377761814105465307136}{2416372265418801343709}\cdot t^{37}-\frac{10549491904788131913587540728642068480}{2416372265418801343709}\cdot t^{35}+\frac{32783914568619040329262016910375690240}{219670205947163758519}\cdot t^{33}-\frac{845287962573129089746973522560474890240}{219670205947163758519}\cdot t^{31}+\frac{16655963458848168993762002923602095339520}{219670205947163758519}\cdot t^{29}-\frac{252643193027286915978811703283250192634880}{219670205947163758519}\cdot t^{27}+\frac{2957966046807717424111639674488725156761600}{219670205947163758519}\cdot t^{25}-\frac{26699794738329453386773994900511200993088000}{219670205947163758519}\cdot t^{23}+\frac{184898704265360067998260184458000146236208000}{219670205947163758519}\cdot t^{21}-\frac{973860371412378229092277490659494029683560000}{219670205947163758519}\cdot t^{19}+\frac{3850847761605773717215529183562715650943800000}{219670205947163758519}\cdot t^{17}-\frac{11225554048030697176739330266455528594615240000}{219670205947163758519}\cdot t^{15}+\frac{23528910270774553002206159185279205971264867500}{219670205947163758519}\cdot t^{13}-\frac{34260729427931527072067886354433864906922681250}{219670205947163758519}\cdot t^{11}+\frac{33016408607003353812065688818842780554127927500}{219670205947163758519}\cdot t^9-\frac{19604772644036946450197982700603702021923706875}{219670205947163758519}\cdot t^7+\frac{25621059462642942356182575706119494496350859375}{878680823788655034076}\cdot t^5-\frac{7530623484111515034703313166062955126966665625}{1757361647577310068152}\cdot t^3+\frac{315985856650052961811842870386999345319178125}{1757361647577310068152}\cdot t$

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.