arXiv subjects

Slobodan B. Tričković

Publications and source records attributed to Slobodan B. Tričković.

3 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↗