Formula:3049

Digital Library of Mathematical Functions ID 7.5.E5

${\displaystyle{\displaystyle e^{-\frac{1}{2}\pi iz^{2}}\mathcal{F}\left(z\right)=\mathrm{g}\left(z\right)+i\mathrm{f}\left(z\right).}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{f}\left(\NVar{z}\right)}}$: auxiliary function for Fresnel integrals
• ${\displaystyle{\displaystyle\mathrm{g}\left(\NVar{z}\right)}}$: auxiliary function for Fresnel integrals
• ${\displaystyle{\displaystyle\mathcal{F}\left(\NVar{z}\right)}}$: Fresnel integral
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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