Rule: Q[4, 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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^{14}-\frac{3816}{7}\cdot t^{12}+\frac{44964}{7}\cdot t^{10}-\frac{225630}{7}\cdot t^8+68715\cdot t^6-\frac{108945}{2}\cdot t^4+\frac{46845}{4}\cdot t^2-\frac{2835}{8}$
• $P_3$:
  $16\cdot t^{34}-\frac{13504051276154748796470880420344}{3642441958493277806607614783}\cdot t^{32}+\frac{1346497748950455199174604072320056}{3642441958493277806607614783}\cdot t^{30}-\frac{536139807588757901405781198367564620}{25497093709452944646253303481}\cdot t^{28}+\frac{213661811712597515665803399061644129270}{280468030803982391108786338291}\cdot t^{26}-\frac{400732766061689804622719804223155129565}{21574463907998645469906641407}\cdot t^{24}+\frac{13544076590213559875706441760620525810315}{43148927815997290939813282814}\cdot t^{22}-\frac{597822049427129716729423882520964644470755}{160267446173704223490735050452}\cdot t^{20}+\frac{5016361300140195844151106836461343344311825}{160267446173704223490735050452}\cdot t^{18}-\frac{29592000893334893311563654455103289138307325}{160267446173704223490735050452}\cdot t^{16}+\frac{969545860327901381981427334783270033759495575}{1282139569389633787925880403616}\cdot t^{14}-\frac{415012083946719078871547398147359840735602025}{197252241444559044296289292864}\cdot t^{12}+\frac{137952081591962294754448030223379935247554325}{35864043899010735326598053248}\cdot t^{10}-\frac{315289778727625744381733115282739306107747375}{71728087798021470653196106496}\cdot t^8+\frac{59636437690981988342098652131949852564224875}{20493739370863277329484601856}\cdot t^6-\frac{40542643089654694689062552847811835360117625}{40987478741726554658969203712}\cdot t^4+\frac{22674878655728214539314553393680084053993375}{163949914966906218635876814848}\cdot t^2-\frac{1255094291201017792255717299740481308128875}{327899829933812437271753629696}$

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.