This paper reviews the Fourier-series method for calculating cumulative distribution functions (cdf’s) and probability mass functions (pmf’s) by numerically inverting characteristic functions, Laplace transforms and generating functions. Some variants of the Fourier-series method are remarkably easy to use, requiring programs of less than fifty lines. The Fourier-series method can be interprete...

Abstract. The purpose of this paper is to consider a new generalization of the Hurwitz zeta function. Generating functions, Mellin transform, and a series identity are obtained for this generalized class of functions. Some of the results are used to provide a further generalization of the Lambert transform. Relevance with various known results are depicted invariably. Multivariable extensions a...

Human activity recognition is attracting a lot of attention in the computer vision domain. In this paper we present a novel human activity recognition method based on transform and Fourier Mellin Transform (FMT). Firstly, we convert the original image sequence to the Radon domain, get the transform curves by transform. Then we extract the Rotation-Scaling-Translation (RST) invariant features by...

A unitary signal transformation that is covariant by translation to scale changes (di-lations and compressions) in the signal is formulated and justiied. Unlike the Mellin transform, which is invariant to scale changes, this new transform is a true indicator of the scale content of a signal.

In this article we provide integral representations for the Dirichlet beta and Riemann zeta functions, which are obtained by combining Mellin transform with the fractional Fourier transform. As an application of these integral formulas we derive tractable expansions of these L-functions in the series of Meixner-Pollaczek polynomials and rising factorials.

Making use of inverse Mellin transform techniques for analytical continuation, an elegant proof and an extension of the zeta function regularization theorem is obtained. No series commutations are involved in the procedure; nevertheless the result is naturally split into the same three contributions of very different nature, i.e. the series of Riemann zeta functions and the power and negative e...