Formula:4825

Digital Library of Mathematical Functions ID 12.7.E5

${\displaystyle{\displaystyle U\left(\tfrac{1}{2},z\right)=D_{-1}\left(z\right)=\sqrt{\tfrac{1}{2}\pi}\,e^{\frac{1}{4}z^{2}}\operatorname{erfc}\left(z/\sqrt{2}\right),}}$

Symbols List

• ${\displaystyle{\displaystyle D_{\NVar{\nu}}\left(\NVar{z}\right)}}$: parabolic cylinder function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\operatorname{erfc}\NVar{z}}}$: complementary error function
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}$:
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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