Rule: Q[5, 8, 18]

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.

• $P_1$:
  $t^5-10\cdot t^3+15\cdot t$
• $P_2$:
  $t^{13}-\frac{170}{3}\cdot t^{11}+\frac{3251}{3}\cdot t^9-8652\cdot t^7+29631\cdot t^5-41790\cdot t^3+19215\cdot t$
• $P_3$:
  $t^{31}-\frac{14560699451931256481266962557}{40215459959405427123553269}\cdot t^{29}+\frac{208192419144785290304382557497}{3655950905400493374868479}\cdot t^{27}-\frac{756953499128921200244292865928631}{147456686517819899453028653}\cdot t^{25}+\frac{217319278577776516924500879491609781}{737283432589099497265143265}\cdot t^{23}-\frac{1671619897514945905401784062267609201}{147456686517819899453028653}\cdot t^{21}+\frac{16964518509749657889881901613814615919}{56714110199161499789626405}\cdot t^{19}-\frac{4024742055578418935400646610482615069767}{737283432589099497265143265}\cdot t^{17}+\frac{50609363231860838759829946716039534848451}{737283432589099497265143265}\cdot t^{15}-\frac{6648683945405770262471749247986651105227}{11342822039832299957925281}\cdot t^{13}+\frac{3413745531139248608387179413785123018943}{1031165639984754541629571}\cdot t^{11}-\frac{12232006451373305981873636314656387158043}{1031165639984754541629571}\cdot t^9+\frac{26081017691726688029653205683168621040853}{1031165639984754541629571}\cdot t^7-\frac{29913211028780989772553228386825592222789}{1031165639984754541629571}\cdot t^5+\frac{15504330826220252140491480150362995600035}{1031165639984754541629571}\cdot t^3-\frac{2442872768781915414820215587646931237335}{1031165639984754541629571}\cdot t$

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.