Berndt, Bruce C.Bruce C.BerndtDixit, AtulAtulDixitGupta, RajatRajatGuptaZaharescu, AlexandruAlexandruZaharescu2025-08-312025-08-312023-12-1010.4153/S0008414X220005302-s2.0-85140229715http://repository.iitgn.ac.in/handle/IITG2025/25740We consider two sequences a(n) and, b(n), 1 ≤ n < ∞ generated by Dirichlet series {equation presented} satisfying a familiar functional equation involving the gamma function Γ(s). Two general identities are established. The first involves the modified Bessel function K<inf>μ</inf>(z), and can be thought of as a 'modular' or 'theta' relation wherein modified Bessel functions, instead of exponential functions, appear. Appearing in the second identity are K<inf>μ</inf>(z), the Bessel functions of imaginary argument I<inf>μ</inf>(z), and ordinary hypergeometric functions <inf>2</inf>F<inf>1</inf>(a,b;c;z). Although certain special cases appear in the literature, the general identities are new. The arithmetical functions appearing in the identities include Ramanujan's arithmetical function τ(n), the number of representations of n as a sum of k squares rk(n), and primitive Dirichlet characters Χ(n).falseBessel functions | classical arithmetic functions | functional equationsArticle1800-183010 December 20230arJournal0WOS:000884077900001