Rule: Q[3, 48]

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.

• $P_1$:
  $t^3-3\cdot t$
• $P_2$:
  $t^{51}-\frac{2344976159974179967385637}{1869618530014239455359}\cdot t^{49}+\frac{1356038952177960321962866812}{1869618530014239455359}\cdot t^{47}-\frac{20887300115893944228613338732}{81287762174532150233}\cdot t^{45}+\frac{5081172520297461244752586608810}{81287762174532150233}\cdot t^{43}-\frac{901688530101157535501960961789870}{81287762174532150233}\cdot t^{41}+\frac{121048031415001121260885986877249380}{81287762174532150233}\cdot t^{39}-\frac{12582740730526776869764206564517635180}{81287762174532150233}\cdot t^{37}+\frac{1028277585356073646155476110137832105215}{81287762174532150233}\cdot t^{35}-\frac{66708888101444100572481533794316088178725}{81287762174532150233}\cdot t^{33}+\frac{3455084292229562612940668026891986309736200}{81287762174532150233}\cdot t^{31}-\frac{143217433736985242979932240662863515553691800}{81287762174532150233}\cdot t^{29}+\frac{4749490565217674731815803460634536556897560300}{81287762174532150233}\cdot t^{27}-\frac{125643364803018416055885285028739152614170796900}{81287762174532150233}\cdot t^{25}+\frac{2636796093110563164701654499007410389830874265000}{81287762174532150233}\cdot t^{23}-\frac{43536819690695865143356320653748540562601665755000}{81287762174532150233}\cdot t^{21}+\frac{559120781768415539427274652443133714719483935654375}{81287762174532150233}\cdot t^{19}-\frac{5500373980676034244294564056958520571110258377348125}{81287762174532150233}\cdot t^{17}+\frac{40623582960260492028422761052806148533652014147972500}{81287762174532150233}\cdot t^{15}-\frac{219332757736055236429566263293098151174707964476037500}{81287762174532150233}\cdot t^{13}+\frac{835250393381932344906452608890159377871643186408106250}{81287762174532150233}\cdot t^{11}-\frac{2134793654172795701217515404835618006614566291656268750}{81287762174532150233}\cdot t^9+\frac{3406952870590997959580318455647053804795174727048112500}{81287762174532150233}\cdot t^7-\frac{3031858596583890443738681041427174906383654804941337500}{81287762174532150233}\cdot t^5+\frac{1230425455805217450376678266975759344075171227523390625}{81287762174532150233}\cdot t^3-\frac{143709179564057665903468732002823497258858354358546875}{81287762174532150233}\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.