Bounds for Zeros of Some Special Functions
Bounds for Zeros of Some Special Functions
For $n \geqq 1$ let ${b_n}$ and ${c_n}$ be zeros (ordered by increasing values) of $u(x)$ and $v(x)$, respectively, which are non-trivial solutions of $u'' + p(x)u = 0$ and $v'' + q(x)v = 0$ with continuous $p(x)$ and $q(x)$. It is shown that if ${b_n} - {c_n} \to 0$ …