Rule: Q[1, 16, 28]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{17}-136\cdot t^{15}+3570\cdot t^{13}-46410\cdot t^{11}+\frac{1276275}{4}\cdot t^9-\frac{2297295}{2}\cdot t^7+\frac{16081065}{8}\cdot t^5-\frac{11486475}{8}\cdot t^3+\frac{34459425}{128}\cdot t$
• $P_3$:
  $2\cdot t^{45}-\frac{437043667621911734}{543076105530597}\cdot t^{43}+\frac{74934495009974702599}{514493152607934}\cdot t^{41}-\frac{76962581054430009766219}{4887684949775373}\cdot t^{39}+\frac{44533267916315144809389911}{39101479598202984}\cdot t^{37}-\frac{6860978641472089027853975197}{117304438794608952}\cdot t^{35}+\frac{1036416474319522765749983733485}{469217755178435808}\cdot t^{33}-\frac{1225597275639659072751977040665}{19550739799101492}\cdot t^{31}+\frac{423843151280171713076240229080105}{312811836785623872}\cdot t^{29}-\frac{369929147687353457090463519128185}{16463780883453888}\cdot t^{27}+\frac{13286119453454671887594009909024595}{46342494338610944}\cdot t^{25}-\frac{65147298648697241271945156317685875}{23171247169305472}\cdot t^{23}+\frac{3909736783859284011870492318363426125}{185369977354443776}\cdot t^{21}-\frac{1170752498253681745714536154487431875}{9756314597602304}\cdot t^{19}+\frac{19948828883813634182550222284743884375}{39025258390409216}\cdot t^{17}-\frac{15621280315556696449851973760119775625}{9756314597602304}\cdot t^{15}+\frac{1123036671520224205242425136711878000625}{312202067123273728}\cdot t^{13}-\frac{1748605286052888997701295084513546164375}{312202067123273728}\cdot t^{11}+\frac{7189897628627433272298320071317771575625}{1248808268493094912}\cdot t^9-\frac{2268168637116558137700590182463994736875}{624404134246547456}\cdot t^7+\frac{6219205748323418114443922714143824526875}{4995233073972379648}\cdot t^5-\frac{904594761764889130230215911900481446875}{4995233073972379648}\cdot t^3+\frac{109505253801035390420274266693525821875}{19980932295889518592}\cdot t$

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.