Properties
- C(x) and S(x) are odd functions of x.
- Using the power series expansions above, the Fresnel integrals can be extended to the domain of complex numbers, and they become analytic functions of a complex variable. The Fresnel integrals can be expressed using the error function as follows:
- C and S are entire functions.
- The integrals defining C(x) and S(x) cannot be evaluated in the closed form in terms of elementary functions, except in special cases. The limits of these functions as x goes to infinity are known:
Read more about this topic: Fresnel Integral
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