Formula:3054

Digital Library of Mathematical Functions ID 7.5.E10

${\displaystyle{\displaystyle\mathrm{g}\left(z\right)\pm i\mathrm{f}\left(z\right)=\tfrac{1}{2}(1\pm i)e^{\zeta^{2}}\operatorname{erfc}\zeta.}}$

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
• ${\displaystyle{\displaystyle\operatorname{erfc}\NVar{z}}}$: complementary error function
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\zeta}}$: change of variable (locally)
 

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