Rule: Q[2, 10, 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.

• $P_1$:
  $t^2-1$
• $P_2$:
  $t^{12}-\frac{8477}{152}\cdot t^{10}+\frac{155745}{152}\cdot t^8-\frac{563535}{76}\cdot t^6+\frac{1500975}{76}\cdot t^4-\frac{2132865}{152}\cdot t^2+\frac{110565}{152}$
• $P_3$:
  $t^{30}-\frac{464618060298268536335966586445135906597}{1510707726075761956687631283277606696}\cdot t^{28}+\frac{2689013561339001659670010100492528117988069}{66471139947333526094255776464214694624}\cdot t^{26}-\frac{18126119742904992861155606131661140908665775}{6042830904303047826750525133110426784}\cdot t^{24}+\frac{4626139847561917955504115562470385626001490925}{33235569973666763047127888232107347312}\cdot t^{22}-\frac{141096801233457726833832326626737963682902554055}{33235569973666763047127888232107347312}\cdot t^{20}+\frac{5785532123181821522983553381005568090890277273895}{66471139947333526094255776464214694624}\cdot t^{18}-\frac{80209415453304433252532377185263112648459781372335}{66471139947333526094255776464214694624}\cdot t^{16}+\frac{186703221951558124954181778344890941595922857010775}{16617784986833381523563944116053673656}\cdot t^{14}-\frac{143156601053717313816157705761668880910364596524600}{2077223123354172690445493014506709207}\cdot t^{12}+\frac{1627485608481292279186219674333527670320398759751625}{6042830904303047826750525133110426784}\cdot t^{10}-\frac{3842818708316602397948655734485184850115028601096825}{6042830904303047826750525133110426784}\cdot t^8+\frac{2522153966038588395444331971006466288506839097044175}{3021415452151523913375262566555213392}\cdot t^6-\frac{1604946066155351300643462628219311554610840701516625}{3021415452151523913375262566555213392}\cdot t^4+\frac{770275830893755016484418219025941920934367496205875}{6042830904303047826750525133110426784}\cdot t^2-\frac{34004406526346698253109822054542197634570572324875}{6042830904303047826750525133110426784}$

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.