Formula:8962

Digital Library of Mathematical Functions ID 28.8.E4

${\displaystyle{\displaystyle U_{m}(\xi)\sim D_{m}\left(\xi\right)-\frac{1}{2^{6}h}\left(D_{m+4}\left(\xi\right)-4!\dbinom{m}{4}D_{m-4}\left(\xi\right)\right)+\frac{1}{2^{13}h^{2}}\left(D_{m+8}\left(\xi\right)-2^{5}(m+2)D_{m+4}\left(\xi\right)+4!\,2^{5}(m-1)\dbinom{m}{4}D_{m-4}\left(\xi\right)+8!\genfrac{(}{)}{0.0pt}{}{m}{8}D_{m-8}\left(\xi\right)\right)+\cdots,}}$

Symbols List

• ${\displaystyle{\displaystyle D_{\NVar{\nu}}\left(\NVar{z}\right)}}$: parabolic cylinder function
• ${\displaystyle{\displaystyle\sim}}$:
• ${\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle m}}$: integer
• ${\displaystyle{\displaystyle h}}$: parameter
• ${\displaystyle{\displaystyle\xi}}$: variable
 

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