Rule: Q[2, 7, 22]

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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^9-\frac{346}{5}\cdot t^7+\frac{1743}{5}\cdot t^5-\frac{1113}{2}\cdot t^3+\frac{399}{2}\cdot t$
• $P_3$:
  $4\cdot t^{31}-\frac{2920374384609013514657792078653}{3904915415107666622223936915}\cdot t^{29}+\frac{8041901676266676382436760385583753}{132767124113660665155613855110}\cdot t^{27}-\frac{331195052269676336499181178054457197}{118015221434365035693878982320}\cdot t^{25}+\frac{82055247883143004461000450083856017165}{991327860048666299828583451488}\cdot t^{23}-\frac{3246140248777571012182912994628889581935}{1982655720097332599657166902976}\cdot t^{21}+\frac{4210438466998417746953493509541979108465}{188824354294984057110206371712}\cdot t^{19}-\frac{586953887803066500665781963577244487195}{2776828739632118486914799584}\cdot t^{17}+\frac{30960600010240643947552909561046053882545}{22214629917056947895318396672}\cdot t^{15}-\frac{280716368844760760210308125539800415363325}{44429259834113895790636793344}\cdot t^{13}+\frac{1708461983397182388502263244930665088920675}{88858519668227791581273586688}\cdot t^{11}-\frac{13401282238554224335199442158767674246255225}{355434078672911166325094346752}\cdot t^9+\frac{31706871247875302668932220875649590073946925}{710868157345822332650188693504}\cdot t^7-\frac{40576475554716825828648518123433562033330575}{1421736314691644665300377387008}\cdot t^5+\frac{23056085060108313266668173710515747405147125}{2843472629383289330600754774016}\cdot t^3-\frac{1849077059374323896631123075777392766559875}{2843472629383289330600754774016}\cdot t$

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.