Rule: Q[6, 34]

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.

• $P_1$:
  $64\cdot t^6-480\cdot t^4+720\cdot t^2-120$
• $P_2$:
  $64\cdot t^{40}-\frac{141834330436042694831355286864}{6416079694967971826817497}\cdot t^{38}+\frac{637037927188843320757767442224184}{186066311154071182977707413}\cdot t^{36}-\frac{410378924499380771828059414467315500}{1302464178078498280843951891}\cdot t^{34}+\frac{25074236396765863920464920670828632230}{1302464178078498280843951891}\cdot t^{32}-\frac{1076677685353553674203343393496721217020}{1302464178078498280843951891}\cdot t^{30}+\frac{1156956351907157237814478958192744706330}{44912557864775802787722479}\cdot t^{28}-\frac{3806723924547664742843253641977369598685}{6416079694967971826817497}\cdot t^{26}+\frac{65402061774094819452536091891521255283750}{6416079694967971826817497}\cdot t^{24}-\frac{6722244714051452325752811781421330039308875}{51328637559743774614539976}\cdot t^{22}+\frac{128764779972484355766026537381917154114626125}{102657275119487549229079952}\cdot t^{20}-\frac{1823026149948664126133116323760498569291138375}{205314550238975098458159904}\cdot t^{18}+\frac{18806952412350374415905021280841092572758618875}{410629100477950196916319808}\cdot t^{16}-\frac{69224469338957311991141869115216843432055365625}{410629100477950196916319808}\cdot t^{14}+\frac{353089288511251506681727414140455970308652219375}{821258200955900393832639616}\cdot t^{12}-\frac{1197370402590347747234274212095992530791143200625}{1642516401911800787665279232}\cdot t^{10}+\frac{5088858567810852833024963246919647865220220701875}{6570065607647203150661116928}\cdot t^8-\frac{12397531148563865978830187740251446795638229608125}{26280262430588812602644467712}\cdot t^6+\frac{7474538858095093525410609147763495751884995796875}{52560524861177625205288935424}\cdot t^4-\frac{1673480434066823468291361415659708278774544365625}{105121049722355250410577870848}\cdot t^2+\frac{58513797397030080965390135162395387659199715625}{210242099444710500821155741696}$

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.