Mellin transform

Noun

Mellin transform (plural Mellin transforms)

1. An integral transform that may be regarded as the multiplicative version of the two-sided Laplace transform.
   • This chapter is concerned with the theory and applications of the Mellin transform. We derive the Mellin transform and its inverse from the complex Fourier transform. This is followed by several examples and the basic operational properties of Mellin transforms.1995, Lokenath Debnath, Integral Transforms and Their Applications, CRC Press, page 211
   • If X is a positive random variable with density function f(x), the Mellin transform M(s) gives the (s-l)th moment of X. Hence Theorem 8.2.6 gives the Mellin transform of W evaluated at s=h+1; that is,
     M(h+1)=E(Wʰ).
     The inverse Mellin transform gives the density function of W.2005, Robb J. Muirhead, Aspects of Multivariate Statistical Theory, John Wiley & Sons, page 303