The author solves the central connection problem for the double confluent Heun equation
where denotes the differential operator . By Laplace transform, the equation is reduced to a special confluent Heun equation. For the last equation the problem was solved by D. Schmidt and G. Wolf [In: A. Ronveux (ed.). Heun’s differential equations, Oxford (1995; Zbl 0847.34006) and In: Alavi, Yousev (ed.) et al., Trends and developments in ordinary differential equations. Proceedings of the international symposium, Kalamazoo, 293-303 (1994; Zbl 0902.34002)]. The coefficients of the central connection matrix are computed by limit formulae obtained by the author.