Rule: Q[6, 9, 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.

• $P_1$:
  $t^6-15\cdot t^4+45\cdot t^2-15$
• $P_2$:
  $t^{15}-\frac{13845}{191}\cdot t^{13}+\frac{360405}{191}\cdot t^{11}-\frac{4272555}{191}\cdot t^9+\frac{24327405}{191}\cdot t^7-\frac{64538775}{191}\cdot t^5+\frac{68923575}{191}\cdot t^3-\frac{18129825}{191}\cdot t$
• $P_3$:
  $t^{31}-\frac{57010117328160707221839485390631909655}{127678172195960946379309627115979517}\cdot t^{29}+\frac{10257982309944094849354605018951121519195}{127678172195960946379309627115979517}\cdot t^{27}-\frac{3027010787425551134847140550639714279302615}{383034516587882839137928881347938551}\cdot t^{25}+\frac{183741273049907803609459804404965766302791475}{383034516587882839137928881347938551}\cdot t^{23}-\frac{7313260173914925160739443947925733717284228625}{383034516587882839137928881347938551}\cdot t^{21}+\frac{197042092115289485868836481827746087311830959525}{383034516587882839137928881347938551}\cdot t^{19}-\frac{3646561598011138324056834849627177832302053512075}{383034516587882839137928881347938551}\cdot t^{17}+\frac{46446025834352566579721941475075622655427691161125}{383034516587882839137928881347938551}\cdot t^{15}-\frac{134489432478225917549691005099173615145785246235125}{127678172195960946379309627115979517}\cdot t^{13}+\frac{780492772593427554317977809703175091245115100816625}{127678172195960946379309627115979517}\cdot t^{11}-\frac{265690651878126795786194982639169187580326050571125}{11607106563269176943573602465089047}\cdot t^9+\frac{608079922581907564869728793471397218483337468364625}{11607106563269176943573602465089047}\cdot t^7-\frac{781520970338406505246184963233696013614138600216875}{11607106563269176943573602465089047}\cdot t^5+\frac{486096311613285833355945554098452142978708378284375}{11607106563269176943573602465089047}\cdot t^3-\frac{100252484253233875494515769323786003044777611875625}{11607106563269176943573602465089047}\cdot t$

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.