Zeros of a cross-product of the Coulomb wave and Tricomi hypergeometric functions

Motivated by a problem related to conditions for the existence of clines in genetics, in this note our aim is to show that the positive zeros of a cross-product of the regular Coulomb wave function and the Tricomi hypergeometric function are increasing with respect to the order. In particular, this implies that the eigenvalues of a boundary value problem are increasing with the dimension.