Formula:3079

Digital Library of Mathematical Functions ID 7.7.E11

${\displaystyle{\displaystyle\mathrm{g}\left(z\right)=\frac{1}{\pi\sqrt{2}}\int_{0}^{\infty}\frac{\sqrt{t}e^{-\pi z^{2}t/2}}{t^{2}+1}\mathrm{d}t,}}$

Constraint(s)

${\displaystyle{\displaystyle|\operatorname{ph}z|\leq\frac{1}{4}\pi}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{g}\left(\NVar{z}\right)}}$: auxiliary function for Fresnel integrals
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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