Formula:4827

Digital Library of Mathematical Functions ID 12.7.E7

${\displaystyle{\displaystyle U\left(n+\tfrac{1}{2},z\right)=e^{\frac{1}{4}z^{2}}\mathit{Hh}_{n}\left(z\right)=\sqrt{\pi}\,2^{\frac{1}{2}(n-1)}e^{\frac{1}{4}z^{2}}\mathop{\mathrm{i}^{n}\mathrm{erfc}}\left(z/\sqrt{2}\right),}}$

Constraint(s)

${\displaystyle{\displaystyle n=-1,0,1,\dots}}$

Symbols List

• ${\displaystyle{\displaystyle\mathit{Hh}_{\NVar{n}}\left(\NVar{z}\right)}}$: probability function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}$:
• ${\displaystyle{\displaystyle\mathop{\mathrm{i}^{\NVar{n}}\mathrm{erfc}}\left(\NVar{z}\right)}}$: repeated integrals of the complementary error function
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
 

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