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.

• $P_1$:
  $t^6-15\cdot t^4+45\cdot t^2-15$
• $P_2$:
  $t^{40}-\frac{8864645652252668426959705429}{12832159389935943653634994}\cdot t^{38}+\frac{79629740898605415094720930278023}{372132622308142365955414826}\cdot t^{36}-\frac{102594731124845192957014853616828875}{2604928356156996561687903782}\cdot t^{34}+\frac{12537118198382931960232460335414316115}{2604928356156996561687903782}\cdot t^{32}-\frac{538338842676776837101671696748360608510}{1302464178078498280843951891}\cdot t^{30}+\frac{1156956351907157237814478958192744706330}{44912557864775802787722479}\cdot t^{28}-\frac{7613447849095329485686507283954739197370}{6416079694967971826817497}\cdot t^{26}+\frac{261608247096379277810144367566085021135000}{6416079694967971826817497}\cdot t^{24}-\frac{6722244714051452325752811781421330039308875}{6416079694967971826817497}\cdot t^{22}+\frac{128764779972484355766026537381917154114626125}{6416079694967971826817497}\cdot t^{20}-\frac{1823026149948664126133116323760498569291138375}{6416079694967971826817497}\cdot t^{18}+\frac{18806952412350374415905021280841092572758618875}{6416079694967971826817497}\cdot t^{16}-\frac{138448938677914623982283738230433686864110731250}{6416079694967971826817497}\cdot t^{14}+\frac{706178577022503013363454828280911940617304438750}{6416079694967971826817497}\cdot t^{12}-\frac{2394740805180695494468548424191985061582286401250}{6416079694967971826817497}\cdot t^{10}+\frac{5088858567810852833024963246919647865220220701875}{6416079694967971826817497}\cdot t^8-\frac{12397531148563865978830187740251446795638229608125}{12832159389935943653634994}\cdot t^6+\frac{7474538858095093525410609147763495751884995796875}{12832159389935943653634994}\cdot t^4-\frac{1673480434066823468291361415659708278774544365625}{12832159389935943653634994}\cdot t^2+\frac{58513797397030080965390135162395387659199715625}{12832159389935943653634994}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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