The product of two functions of bounded value distribution
An entire function is said to be of bounded value distribution (B.V.D.) if any complex value is taken a certain number P(R) times at most in any disc of radius R. Every entire solution of a linear differential equation with rational coefficients bounded at infinity is of B.V.D. (Turán, Hayman, Shah). For instance, the Bessel function \(J_ n(z)\) is of B.V.D. Here it is shown that the product \(J_ mJ_ n\) satisfies such a differential equation of order 4. Thus, it is of B.V.D.
scientific article; zbMATH DE number 3966633