Rule: Q[1, 4, 8, 16]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^5-10\cdot t^3+\frac{15}{2}\cdot t$
• $P_3$:
  $2\cdot t^{13}-\frac{170}{3}\cdot t^{11}+\frac{3251}{6}\cdot t^9-2163\cdot t^7+\frac{29631}{8}\cdot t^5-\frac{20895}{8}\cdot t^3+\frac{19215}{32}\cdot t$
• $P_4$:
  $2\cdot t^{29}-\frac{42089393394686530251326}{139527960992289822237}\cdot t^{27}+\frac{895873287982445463318218581}{46044227127455641338210}\cdot t^{25}-\frac{48836935412609831205713497639}{69066340691183462007315}\cdot t^{23}+\frac{8876737578247005811868386501051}{552530725529467696058520}\cdot t^{21}-\frac{44108775347382017021123663331133}{184176908509822565352840}\cdot t^{19}+\frac{352601232147804563918755868779777}{147341526807858052282272}\cdot t^{17}-\frac{2965495067362080962531497949951299}{184176908509822565352840}\cdot t^{15}+\frac{14202892543910658710228117364411877}{196455369077144069709696}\cdot t^{13}-\frac{3783230591099896361804617757150177}{17859579007013097246336}\cdot t^{11}+\frac{27837716764475429834380073083743739}{71438316028052388985344}\cdot t^9-\frac{219024916593385168364279599608645}{517668956725017311488}\cdot t^7+\frac{23393352488929388152056163419837621}{95251088037403185313792}\cdot t^5-\frac{6111560775481539139195129854709005}{95251088037403185313792}\cdot t^3+\frac{1939616588277833633824116159509265}{381004352149612741255168}\cdot t$

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.