On a Remarkable Sequence of Bessel Matrices

A sequence of matrices whose elements are modified Bessel functions of the first kind is considered. Such a sequence arises when studying certain ordinary linear homogeneous second-order differential equations belonging to the family of double confluent Heun equations. The conjecture that these matrices are nonsingular is discussed together with its application to the problem of the existence of solutions analytic at the singular point of the equation referred to above.