A Double Integral Containing the Fresnel Integral Function Sx: Derivation and Computation. (15th March 2022) - Reynolds, Robert; Stauffer, Allan
Abstract : A two-dimensional integral containing S x is derived. S x is the Fresnel integral function, and the double integral is taken over the range 0 < x < ∞ and 0 < y < ∞ . A representation in terms of the Hurwitz–Lerch zeta function is derived, from which other special function representations can be evaluated. All the results in this work are new.