Mellin transform

English Alternative forms en Mellin-transform attributive use Etymology Named after Finnish mathematician Hjalmar Mellin. Noun en analysis number theory statistics An integral transform that may be regarded as the multiplicative version of the two-sided Laplace transform. en 1995 Lokenath Debnath Integral Transforms and Their Applications https://books.google.com.au/books?id=KFG4G4tmURoC&pg=PA211&dq=%22Mellin+transform%22%7C%22Mellin+transforms%22&hl=en&sa=X&ved=0ahUKEwjD0Yy2x6PeAhWFKn0KHerYAbQQ6AEIbTAN#v=onepage&q=%22Mellin%20transform%22%7C%22Mellin%20transforms%22&f=false 211 CRC Press 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. 2005, Robb J. Muirhead, Aspects of Multivariate Statistical Theory, John Wiley & Sons, page 303, If is a positive random variable with density function , the Mellin transform gives the th moment of . Hence Theorem 8.2.6 gives the Mellin transform of evaluated at ; that is, . The inverse Mellin transform gives the density function of . en 2008 w:Bruce C. Berndt; Marvin Knopp Marvin I. Knopp Hecke's Theory of Modular Forms and Dirichlet Series World Scientific https://books.google.com.au/books?id=DGhjc6V3FUQC&pg=PA115&dq=%22Mellin+transform%22%7C%22Mellin+transforms%22&hl=en&sa=X&ved=0ahUKEwjD0Yy2x6PeAhWFKn0KHerYAbQQ6AEIpwEwGg#v=onepage&q=%22Mellin%20transform%22%7C%22Mellin%20transforms%22&f=false 115 In Chapters 2 and 7, the Mellin transform of the exponential function and the inverse Mellin transform of the Gamma function play key roles in demonstrating the equivalence of the modular relation and the functional equation. In proving the identities in this chapter, Mellin transforms also play central roles. Further reading Mellin inversion theorem Perron's formula Asymptotic expansion Fourier transform Laplace transform Dirichlet series Riemann zeta function Mellin transform on Encyclopedia of Mathematics Mellin Transform on MathWorld Wolfram MathWorld en eponyms