  We derive properties of powers of a function satisfying a second-order linear
differential equation. In particular we prove that the n-th power of the
function satisfies an (n+1)-th order differential equation and give a simple
method for obtaining the differential equation. Also we determine the exponents
of the differential equation and derive a bound for the degree of the
polynomials, which are coefficients in the differential equation. The bound
corresponds to the order of differential equation satisfied by the n-fold
convolution of the Fourier transform of the function. These results are applied
to some probability density functions used in statistics.
