Author’s abstract. This paper considers the asymptotic form of solutions of the equation
for real values of x and h and large values of u. Attention is focussed on the solution
(x,u) that tends to zero as
and for values of u in the half plane Re(u)
. The basic asymptotic formulas that appear require the determination of an elliptic integral but, when u is large, it is shown how this integral can be suitably approximated by elementary functions. An asymptotic formula is derived which gives the large zeros of the function
(x,u) regarded as a function of u, the quantity x being supposed prescribed and positive.