Rule: Q[6, 30]

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.

• $P_1$:
  $t^6-15\cdot t^4+45\cdot t^2-15$
• $P_2$:
  $t^{36}-\frac{2656452308215196570215635}{4977785708490330089042}\cdot t^{34}+\frac{625640165232806891941277085}{4977785708490330089042}\cdot t^{32}-\frac{172027226690063622239443368945}{9955571416980660178084}\cdot t^{30}+\frac{15391729136310544717591922053875}{9955571416980660178084}\cdot t^{28}-\frac{72786415058495527276892764988235}{765813185921589244468}\cdot t^{26}+\frac{3165176191261639109995471976020125}{765813185921589244468}\cdot t^{24}-\frac{98795812568849147272809378441227625}{765813185921589244468}\cdot t^{22}+\frac{2224289382915994064949739918865128875}{765813185921589244468}\cdot t^{20}-\frac{1895942383864188837719148376050290625}{40305957153767854972}\cdot t^{18}+\frac{21879332220218868759292261099503573375}{40305957153767854972}\cdot t^{16}-\frac{177001108207600483457380738004604733125}{40305957153767854972}\cdot t^{14}+\frac{979752939817725556365996556823894889375}{40305957153767854972}\cdot t^{12}-\frac{3583217614676060125820730780642238576875}{40305957153767854972}\cdot t^{10}+\frac{8218734850027817475251502850482658078125}{40305957153767854972}\cdot t^8-\frac{10862590858832592833964209830320808820625}{40305957153767854972}\cdot t^6+\frac{7080913132669906868124047827249262184375}{40305957153767854972}\cdot t^4-\frac{1622514288489944788399913056132416590625}{40305957153767854972}\cdot t^2+\frac{44214631502094292917589239503860059375}{40305957153767854972}$

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.