在数学中，Mellin 变换是一种以幂函数为核的积分变换。定义式如下：

而其逆变换为

Mellin 变换有许多应用，例如可以证明黎曼ζ函数的函数方程。

In mathematics, the Mellin transform is an integral transform that may be regarded as the multiplicative version of the two-sided Laplace transform. This integral transform is closely connected to the theory of Dirichlet series, and is often used in number theory, mathematical statistics, and the theory of asymptotic expansions; it is closely related to the Laplace transform and the Fourier transform, and the theory of the gamma function and allied special functions.