Airy函数的零点分布

The Distribution of Zeros of Airy Function

作为二阶微分方程 f″-zf=0的解 ,Airy函数有可列个零点且均为负数 ,本文借助 Macdonal函数 ,证明了这一重要结论 .其证明过程不涉及整函数阶的问题 ,是一种较为初等的证明方法 .

As a solution of differential equation f″-zf= 0 ,Airy function has a countable set of zeros. This important conclusion is pro ved by using Macdonal function in this article, and the process does not concer n the order of integral function. It is a kind of more elementary method.