Formula:3053

Digital Library of Mathematical Functions ID 7.5.E9

${\displaystyle{\displaystyle C\left(z\right)\pm iS\left(z\right)=\tfrac{1}{2}(1\pm i)\left(1-e^{\pm\frac{1}{2}\pi iz^{2}}w\left(i\zeta\right)\right).}}$

Symbols List

• ${\displaystyle{\displaystyle C\left(\NVar{z}\right)}}$: Fresnel integral
• ${\displaystyle{\displaystyle S\left(\NVar{z}\right)}}$: Fresnel integral
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle w\left(\NVar{z}\right)}}$: Faddeeva (or Faddeyeva) 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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