Rule: Q[1, 14, 24]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{15}-105\cdot t^{13}+\frac{4095}{2}\cdot t^{11}-\frac{75075}{4}\cdot t^9+\frac{675675}{8}\cdot t^7-\frac{2837835}{16}\cdot t^5+\frac{4729725}{32}\cdot t^3-\frac{2027025}{64}\cdot t$
• $P_3$:
  $2\cdot t^{39}-\frac{62014200483}{111167107}\cdot t^{37}+\frac{77025650239581}{1111671070}\cdot t^{35}-\frac{2257924922559929}{444668428}\cdot t^{33}+\frac{109074349464664353}{444668428}\cdot t^{31}-\frac{7352238606233989545}{889336856}\cdot t^{29}+\frac{357028515457686008475}{1778673712}\cdot t^{27}-\frac{12720183299149359966471}{3557347424}\cdot t^{25}+\frac{83893300277359757374575}{1778673712}\cdot t^{23}-\frac{1642808824748037965039175}{3557347424}\cdot t^{21}+\frac{23799731954347695379138875}{7114694848}\cdot t^{19}-\frac{63205302381877775926335375}{3557347424}\cdot t^{17}+\frac{7759768228261170916821555375}{113835117568}\cdot t^{15}-\frac{42054573662072878492643124375}{227670235136}\cdot t^{13}+\frac{155858717808726299157448783125}{455340470272}\cdot t^{11}-\frac{377011515627116873509997615625}{910680940544}\cdot t^9+\frac{1111063705148282649675579793125}{3642723762176}\cdot t^7-\frac{895841061297567707935216729125}{7285447524352}\cdot t^5+\frac{329101417712933649800160519375}{14570895048704}\cdot t^3-\frac{36802618766800322253517074375}{29141790097408}\cdot t$

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.