Sun Kim (김선), Two identities in Ramanujan’s Lost Notebook with Bessel function series
Room 1401, Bldg. E6-1, KAISTOn page 335 in his lost notebook, Ramanujan recorded without proofs two identities involving finite trigonometric sums and doubly infinite series of Bessel functions. We proved each of these identities under three different interpretations for the double series, and showed that they are intimately connected with the classical circle and divisor problems in number theory. …