Formula:6498

Digital Library of Mathematical Functions ID 18.18.E11

${\displaystyle{\displaystyle\frac{(a_{1}^{2}+\dots+a_{r}^{2})^{\frac{1}{2}n}}{n!}H_{n}\left(\frac{a_{1}x_{1}+\cdots+a_{r}x_{r}}{(a_{1}^{2}+\cdots+a_{r}^{2})^{\frac{1}{2}}}\right)=\sum_{m_{1}+\cdots+m_{r}=n}\frac{a_{1}^{m_{1}}\cdots a_{r}^{m_{r}}}{m_{1}!\cdots m_{r}!}H_{m_{1}}\left(x_{1}\right)\cdots H_{m_{r}}\left(x_{r}\right).}}$

Symbols List

• ${\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}$: Hermite polynomial
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle m}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle a_{n}}}$: 18.18.E1
• ${\displaystyle{\displaystyle x}}$: real variable
 

Resources that cite this formula

No records found.