Formula:6419

Digital Library of Mathematical Functions ID 18.15.E27

${\displaystyle{\displaystyle H_{n}\left(x\right)=\lambda_{n}e^{\frac{1}{2}x^{2}}\left(\sum_{m=0}^{M-1}\frac{u_{m}(x)\cos\omega_{n,m}(x)}{\mu^{\frac{1}{2}m}}+O\left(\frac{1}{\mu^{\frac{1}{2}M}}\right)\right),}}$

Symbols List

• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}$: Hermite polynomial
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle m}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle\omega_{n,m}(x)}}$: 18.15.E26
• ${\displaystyle{\displaystyle x}}$: real variable
 

Resources that cite this formula

No records found.