方程f″－zf＝0解的零点

THE ZERO POINTS OF THE SOLUTION OF f"─zf=0

首先于实数域内．用ｓｔｕｒｍ比较定理证得ｆ＂－ｘｆ＝０的非平凡解的零点集含有可列个负数；尔后延拓到复数域内，把特解Ａｉｒｙ积分Ａｉ（ｚ）用Ｍａｃｄｏｎａｌｄ函数表示．通过复围线积分计算证得Ａｉ（ｚ）仅有负数的零点，从而获得了ｆ＂－ｚｆ＝０的非平凡解有且仅有可列个负数零点的结论．

First, in the real field,applying the Sturm's the orem,it is proved that every nonordinary solution of f'─xf=0 has countable negative zero points. Next, in the complex field, by use of the Macdonald function representation of Airy integral,it is proved that the special solution Ai(z) of f'─zf=0 only has negative zero points. Finally that every non─ordinary solution of f'-zf=0 has and only has countable negative zero points is obtained.