A Double Integral Containing the Fresnel Integral Function Sx: Derivation and Computation. (15th March 2022)

• Record Type: Journal Article
• Authors: Reynolds, Robert; Stauffer, Allan
• Other Names: Araci Serkan Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2022(2022)
• Publication Date: 2022-03-15
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2022/7044988
• Languages: English
• ISSNs: 2314-4629

Abstract

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.