Tibor Pogany - Profile on Academia.edu (original) (raw)

Papers by Tibor Pogany

DOAJ (DOAJ: Directory of Open Access Journals), Dec 1, 2011

The object of this article is to investigate the Dirichlet averages of the generalized multiindex... more The object of this article is to investigate the Dirichlet averages of the generalized multiindex Mittag-Leffler functions introduced by Saxena and Nishimoto . Representations of such relations are obtained in terms of Riemann-Liouville integrals and hypergeometric functions of several variables. Some interesting special cases of the established results associated with generalized Mittag-Leffler functions due to Srivastava and Tomovski [32] and multi-index Mittag-Leffler functions due to Kiryakova [12] are deduced. Certain results given earlier by Kilbas et al. [8] also follow as special cases of our findings.

Integral Transforms and Special Functions, Feb 13, 2019

The article aims at studying hypergeometric-type mathematical techniques based on the extension o... more The article aims at studying hypergeometric-type mathematical techniques based on the extension of a model previously used to describe the Coulomb self-energy of a uniformly charged a threedimensional cylinder. The associated crossed term integral is investigated and solved by introducing a computational series built from hypergeometric-type terms for different values of parameters involved. The approach considered may be appealing for a broad audience of researchers working in mathematical physics or related disciplines.

Some Mathieu-type series for generalizedH-function associated with a certain class of Feynman integrals

Integral Transforms and Special Functions, Oct 1, 2010

... By Corollary 3.1 and the above equality we can deduce closed integral form expressions forMat... more ... By Corollary 3.1 and the above equality we can deduce closed integral form expressions forMathieu-type series built by polylogarithm function. Remark 3.3. ... Higher Transcendental Functions , Vol. 3, New York: McGraw-Hill. View all references, Chapter 18] and [1010. ...

On Neumann series of Macdonald functions

Integral Transforms and Special Functions, Dec 24, 2022

Markov model in planning the structure of the cargo handling equipment

ABSTRACT

The object of the present talk is to establish a double definite integral representation, and two... more The object of the present talk is to establish a double definite integral representation, and two other indefinite integral expressions for a functional series and its derivative with members containing Jacobi polynomials.

Comptes Rendus Mathematique, Feb 1, 2016

We solve a problem that has remained unsolved since 1936 -the exact distribution of the product o... more We solve a problem that has remained unsolved since 1936 -the exact distribution of the product of two correlated normal random variables. As a by-product, we derive the exact distribution of the mean of the product of correlated normal random variables.

Operations Research Letters, Mar 1, 2018

Second Type Neumann Series Related to Nicholson’s and to Dixon–Ferrar Formula

Trends in mathematics, 2020

The second type Neumann series are considered which building blocks are Nicholson’s and the Dixon... more The second type Neumann series are considered which building blocks are Nicholson’s and the Dixon–Ferrar formulae for $J_\nu ^2(x)+ Y_\nu ^2(x)$. Related closed form double definite integral expressions are established by using the associated Dirichlet’s series Cahen’s Laplace integral for the Nicholson’s case. However, using Dixon–Ferrar formula a double definite integral expression is again obtained. Certain Open Problems are posed in the last section of the chapter.

Remarks on the stable Salpha(beta,gamma,mu(S_ alpha( beta, gamma, mu(Salpha(beta,gamma,mu( distribution$

Methodology and Computing in Applied Probability, 2014

Applied Mathematics Letters, 2011

It is shown that an integral representation for the extension of a general Hurwitz-Lerch zeta fun... more It is shown that an integral representation for the extension of a general Hurwitz-Lerch zeta function recently obtained by [5] is a special case of the closed form integral expression for the Mathieu (a, λ)-series given by Pogány ( ) [1]. As an immediate consequence of the derived results, new integral expressions and related bilateral bounding inequalities are investigated.

On Pólya’s random walk constants

Whittaker-Type Derivative Sampling and (p, q)$$-Order Weighted Differential Operator

Sort-statistics and Operations Research Transactions, Dec 1, 2015

In a recent edition of SORT, Bidram and Nekoukhou proposed a novel class of distributions and der... more In a recent edition of SORT, Bidram and Nekoukhou proposed a novel class of distributions and derived its mathematical properties. Several of the mathematical properties are expressed as single infinite sums or double infinite sums. Here, we show that many of these properties can be expressed in terms of known special functions, functions for which in-built routines are widely available.

Journal of Inequalities in Pure & Applied Mathematics, 2002

In the paper Several integral inequalities published in J. Inequal. Pure Appl. Math. 1 (2000), no... more In the paper Several integral inequalities published in J. Inequal. Pure Appl. Math. 1 (2000), no. 2, Art. 19 (. 001_00.html) and RGMIA Res. Rep. Coll. 2(7) (1999), Art. 9, 1039-1042 () by F. Qi, an open problem was posed. In this article we give the solution and further generalizations of this problem. Reverse inequalities to the posed one are considered and, finally, the derived results are extended to weighted integral inequalities.

arXiv (Cornell University), Feb 2, 2014

The main aim of this article is to characterize and investigate the three parameter exponentiated... more The main aim of this article is to characterize and investigate the three parameter exponentiated exponential Poisson probability distribution EEP(α, β, λ) by giving explicit closed form expressions for its characteristic function φ ξ (t) and moment generating function M ξ (t), and finally, to show that the existing series and integral form expressions for positive integer order moments Eξ ν , ν ∈ N are in fact valid for all ν > 1α, α > 0.

Mathematical Communications, Feb 23, 2021

We derive explicit forms for the three integrals used in Kim and Wand [3] and Wand, Ormerody, Pad... more We derive explicit forms for the three integrals used in Kim and Wand [3] and Wand, Ormerody, Padoan and Frühwirth . The explicit forms involve known special functions for which in-built routines are available.

arXiv (Cornell University), Jul 10, 2016

In this brief note an integral expression is presented for the COM-Poisson renormalization consta... more In this brief note an integral expression is presented for the COM-Poisson renormalization constant Z(λ, ν) on the real axis.

Integral Transforms and Special Functions, May 15, 2018

Definite integral expression is derived for the generalized Le Roytype hypergeometric (α-Mittag-L... more Definite integral expression is derived for the generalized Le Roytype hypergeometric (α-Mittag-Leffler in other words) function p,q , α > 0 on the real axis. Its important corollaries are the oneparameter, the two-parameter Mittag-Leffler function's and the COM-Poisson renormalization constant's integral forms.

IEEE Transactions on Signal Processing, 1991

If F', Fdenote the masses of F( A) at f w , then we have the result Tibor P o g h y Abstract-A ve... more If F', Fdenote the masses of F( A) at f w , then we have the result Tibor P o g h y Abstract-A very tight truncation error upper bound is established for band-limited weakly stationary stochastic processes if the sampling interval is closed. In particular, the magnitude of the upper bound is 0 (N-'* In2 N ) for a symmetric sampling reconstruction from 2 N + 1 sampled values, where q is an arbitrary positive integer. The results are derived with the help of the Bernstein bound on the remainder of a symmetric complex Fourier series of the function exp ( i k t ) . Finally, convergence rates are given for mean square and almost sure sampling reconstructions.