柱坐标系中，本征函数族贝塞尔函数构成完备正交系，因此可作为广义傅里叶级数展开的基. 本文从定义在有限区间[0，ρ0 ]上函数的广义傅里叶级数展开出发，利用贝塞尔函数的渐近展开公式以及贝塞尔函数零点的近似公式，讨论了半无 界空间上函数的傅里叶-贝塞尔积分展开问题，得到了本征函数模方的近似表达式. 当ρ0 趋于无穷时，不连续参量变成连续参量，得到了函数的傅里叶-贝塞尔积分及其展开系数公式.

In cylindrical coordinates，the family of intrinsic Bessel function constitutes a complete orthogonal function series，which can be used as the bases of generalized Fourier expansion. In this paper，starting from the generalized Fourier expansion of a function defined on a finite interval and using the approximate formula of Bessel function and its zero point formula，we discuss the Fourier-Bessel integral expansion of a function defined in semiinfinite space，and get the approximate expression of module square of Bessel function. In the asymptotical situation， discontinuous parameter becomes continuous one，we obtain the Fourier-Bessel integral and coefficient formula of the function.