Rule: Q[1, 10, 20]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{11}-55\cdot t^9+495\cdot t^7-\frac{3465}{2}\cdot t^5+\frac{17325}{8}\cdot t^3-\frac{10395}{16}\cdot t$
• $P_3$:
  $2\cdot t^{31}-\frac{186754615}{487167}\cdot t^{29}+\frac{2813400488215}{88664394}\cdot t^{27}-\frac{88457579680185}{59109596}\cdot t^{25}+\frac{406485657465975}{9093784}\cdot t^{23}-\frac{210299177066181435}{236438384}\cdot t^{21}+\frac{816199322769932175}{67553824}\cdot t^{19}-\frac{15268839072508129275}{135107648}\cdot t^{17}+\frac{196059658160229264675}{270215296}\cdot t^{15}-\frac{131075104234384452375}{41571584}\cdot t^{13}+\frac{751248157705202420325}{83143168}\cdot t^{11}-\frac{2723130989547648656625}{166286336}\cdot t^9+\frac{5846199631464829984875}{332572672}\cdot t^7-\frac{6682280019495599932875}{665145344}\cdot t^5+\frac{3360445036383587315625}{1330290688}\cdot t^3-\frac{480972980473586110125}{2660581376}\cdot t$

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.