arXiv subjects

Miomir S. Stanković

Publications and source records attributed to Miomir S. Stanković.

6 recordsLinked to original sources

arXiv2024

On the Laplace-type transform and its applications

We use the Laplace transform and the Gamma function to introduce a new integral transform and name it the Laplace-type transform possessing the property of mapping a function to a functional sequence, which cannot be achieved by the Laplace transform. In addition, we construct a backward difference as a generalization of the backward difference operator $\nabla$, and connecting it to the Laplace-type transform, we deduce a method for solving difference equations and, relying on classical orthogonal polynomials, for obtaining combinatorial identities. A table of some elementary functions and their images is in the Appendix.

math.CA↗

arXiv2024

Series over Bessel functions as series in terms of Riemann's zeta function

Relying on the Hurwitz formula, we find sums of the series over sine and cosine functions through the Hurwitz zeta function. Using another summation formula for these trigonometric series, we find finite sums of some series over the Riemann zeta function.

math.NT↗

arXiv2024

On closed forms of some trigonometric series

We have derived alternative closed-form formulas for the trigonometric series over sine or cosine functions when the immediate replacement of the parameter appearing in the denominator with a positive integer gives rise to a singularity. By applying the Choi-Srivastava theorem, we reduce these trigonometric series to expressions over Hurwitz's zeta function derivative.

math.CA↗

arXiv2024

Finite and infinite order differential properties of the reduced Mittag--Leffler polynomials

This paper deals with the Mittag-Leffler polynomials (MLP) by extracting their essence which consists of real polynomials with fine properties. They are orthogonal on the real line instead of the imaginary axes for MLP. Beside recurrence relations and zeros, we will point to the closed form of its Fourier transform. The most important contribution consists of the new differential properties, especially the finite and infinite differential equation.

math.CA↗

arXiv2012

Memoization technique for optimizing functions with stochastic input

In this paper we present a strategy for optimization functions with stochastic input. The main idea is to take advantage of decomposition in combination with a look-up table. Deciding what input values should be used for memoization is determined based on the underlying probability distribution of input variables. Special attention is given to difficulties caused by combinatorial explosion.

cs.OH↗

arXiv2010

The deformed exponential functions of two variables

In the recent development in a various disciplines of physics, it is noted the need for including the deformed versions of the exponential functions. In this paper, we consider the deformations which have two purposes: to have them like special cases, and, even more, to acquit their inauguration from mathematical point of view. Really, we will show interesting differential and difference properties of our deformations which are important in forming and explanation of continuous and discrete models of numerous phenomena.

math.CA↗