On Modified Mellin Transform of Generalized Functions

On the Mellin Transform of a Product of Hypergeometric Functions

We obtain representations for the Mellin transform of the product of generalized hypergeometric functions 0 F1[ ax]1 F2[ b2x2] for a;b > 0. The later transform is a generalization of the discontinuous integral of Weber and Schafheitlin; in addition to reducing to other known integrals (for example, integrals involving products of powers, Bessel and Lommel functions), it contains numerous integr...

The Modified Mellin Transform of Powers of the Zeta-function

The modified Mellin transform Zk(s) = ∫ ∞ 1 |ζ( 1 2 + ix)|x dx (k ∈ N) is investigated. Analytic continuation and mean square estimates of Zk(s) are discussed, as well as connections with power moments of |ζ( 1 2 +ix)|, with the special emphasis on the cases k = 1, 2.

Invariant Object Representation with Modified Mellin-Fourier Transform

In this paper is presented a method for invariant 2D object representation based on the MellinFourier Transform (MFT), modified for the application. The so obtained image representation is invariant against 2D rotation, scaling, and translation change (RST). The representation is additionally made invariant to significant contrast and illumination changes. The method is aimed at content-based o...

RSTC-Invariant Object Representation with 2D Modified Mellin-Fourier Transform

In this paper is presented a method for invariant 2D object representation based on the MellinFourier Transform (MFT), modified for the application. The so obtained image representation is invariant against 2D rotation, scaling, and translation change (RST). The representation is additionally made invariant to significant contrast and illumination changes. The method is aimed at content-based o...

Generalized Product Theorem for the Mellin Transform and Its Applications