Zeroes of functions of Fresnel complementary integral type

Abstract

Theoretical upper and lower bounds are established for zeroes of a parametric family of functions which are defined by integrals of the same type as the Fresnel complementary integral. Asymptotic properties for these bounds are obtained as well as monotony properties of the localization intervals. Given the value of the parameter an analytical-numerical procedure is deduced to enclose all zeros of a given function with an a priori error.

Keywords

• Fresnel complementary integrals, zeroes of functions, theoretical bounds for zeroes, gamma distribution