Tibor Pogany - Academia.edu (original) (raw)
Papers by Tibor Pogany
Mathematics, Apr 3, 2023
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
Results in mathematics, Feb 24, 2024
Page 1. 417 DIRECT WEIGHTED LAGRANGE - YEN TYPE INTERPOLATION IN Lt-n,a12 Tihor K. PogAny and Mat... more Page 1. 417 DIRECT WEIGHTED LAGRANGE - YEN TYPE INTERPOLATION IN Lt-n,a12 Tihor K. PogAny and Mato Tudor University of Ri.jeka, Department of Maritime Studies 51000 Rijeka, Studentska 2, Croatia poganj@brod.pfri.hr & tudor@brod.pfri.hr Abstract ...
arXiv (Cornell University), Jun 27, 2016
Motivated by several generalizations of the well-known Mathieu series, the main object of this pa... more Motivated by several generalizations of the well-known Mathieu series, the main object of this paper is to introduce new extension of generalized Mathieu series and to derive various integral representations of such series. Finally master bounding inequality is established using the newly derived integral expression.
arXiv (Cornell University), Apr 12, 2016
This paper is concerned with new results for the circular Eisenstein series εr(z) as well as with... more This paper is concerned with new results for the circular Eisenstein series εr(z) as well as with a novel approach to Hilbert-Eisenstein series hr(z), introduced by Michael Hauss in 1995. The latter turn out to be the product of the hyperbolic sinh-function with an explicit closed form linear combination of digamma functions. The results, which include differentiability properties and integral representations, are established by independent and different argumentations. Highlights are new results on the Butzer-Flocke-Hauss Omega function, one basis for the study of Hilbert-Eisenstein series, which have been the subject of several recent papers.
Integral Transforms and Special Functions, Jun 22, 2016
Introducing the discrete probability distribution by means of the Prabhakar (or the threeparamete... more Introducing the discrete probability distribution by means of the Prabhakar (or the threeparameter Mittag-Leffler) function, we establish explicit expressions for raw and factorial moments and also general fractional order moments. Applying an elementary moment inequality we obtain functional upper bounds for the Turánian difference for Prabhakar function. Finally, a Laguerre inequality is proved and functional upper bound has been given for Laguerreian difference for Prabhakar function.
Mathematics, Aug 29, 2022
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
Anais Da Academia Brasileira De Ciencias, Jun 1, 2010
The five parameter gamma-Weibull distribution has been introduced by Leipnik and Pearce (2004). N... more The five parameter gamma-Weibull distribution has been introduced by Leipnik and Pearce (2004). Nadarajah and Kotz (2007) have simplified it into four parameter form, using hypergeometric functions in some special cases. We show that the probability distribution function, all moments of positive order and the characteristic function of gamma-Weibull distribution of a random variable can be explicitely expressed in terms of the incomplete confluent Fox-Wright Psi-function, which is recently introduced by Srivastava and Pogány (2007). In the same time, we generalize certain results by Nadarajah and Kotz that follow as special cases of our findings.
Tbilisi Mathematical Journal, 2014
This paper deals with the derivation of certain new Pólya-Szegő type inequalities by making use o... more This paper deals with the derivation of certain new Pólya-Szegő type inequalities by making use of the Saigo fractional integral operator. The results obtained cover the same kind of conclusions in the case of Riemann-Liouville and Erdélyi-Kober fractional integral operators.
Applied Mathematics and Computation, Jul 1, 2021
Mathematics
We establish several new functional bounds and uniform bounds (with respect to the variable) for ... more We establish several new functional bounds and uniform bounds (with respect to the variable) for the lower incomplete generalized Fox–Wright functions by means of the representation formulae for the McKay Iν Bessel probability distribution’s cumulative distribution function. New cumulative distribution functions are generated and expressed in terms of lower incomplete Fox–Wright functions and/or generalized hypergeometric functions, whilst in the closing part of the article, related bounding inequalities are obtained for them.
Journal of Mathematical Inequalities
A new generalization of Whittaker function M λ ,μ (z) is introduced and studied by means of the e... more A new generalization of Whittaker function M λ ,μ (z) is introduced and studied by means of the extended multi-index confluent hypergeometric function of the first kind Φ (γ i),p (α i ,β i) introduced in [1]. The related Euler-type integral representation and the Laplace-Mellin and Hankel integral transforms are also presented. Functional two-sided bounding inequality is established for the multi-index Mittag-Leffler function, and in continuation functional lower bound is derived for the associated ML-extended Whittaker function.
Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), 2017
In this paper, motivated by certain recent extensions of the Euler’s beta, Gauss’ hypergeometric ... more In this paper, motivated by certain recent extensions of the Euler’s beta, Gauss’ hypergeometric and confluent hypergeometric functions (see [4]), we extend the Srivastava’s triple hypergeometric function HA by making use of two additional parameters in the integrand. Systematic investigation of its properties including, among others, various integral representations of Euler and Laplace type, Mellin transforms, Laguerre polynomial representation, transformation formulas and a recurrence relation, is presented. Also, by virtue of Luke’s bounds for hypergeometric functions and various bounds upon the Bessel functions appearing in the kernels of the newly established integral representations, we deduce a set of bounding inequalities for the extended Srivastava’s triple hypergeometric function HA,p,q.
Comptes Rendus Mathematique, 2018
On properties and applications of (p, q)-extended τ-hypergeometric functions Sur les propriétés e... more On properties and applications of (p, q)-extended τ-hypergeometric functions Sur les propriétés et applications des fonctions τ-hypergéométriques
Applicable Analysis and Discrete Mathematics, 2017
In 2000 Chen introduced a two-parameter lifetime model and has reported only a few mathematical p... more In 2000 Chen introduced a two-parameter lifetime model and has reported only a few mathematical properties moments, quantile and generating functions, among others. In this article, we derive a power series expansion for newly introduced real upper parameter generalized integro-exponential function Eps(z) extending certain Milgram's findings. By our novel results we derive closed-form expressions for the moments, generating function, R?nyi entropy and power series for the quantile function of the Chen distribution.
Polish Maritime Research, 2018
In the maritime Very High Frequency (VHF) band, there are no systems for transmitting large amoun... more In the maritime Very High Frequency (VHF) band, there are no systems for transmitting large amounts of data. Therefore, it is necessary to develop new systems that would modernize the Global Maritime Distress and Safety System (GMDSS), significantly relieve the Automatic Identification System’s (AIS) communication channels, and set guidelines for the development of communication infrastructure of the e-Navigation. In line with this, analytical and simulation models of the maritime VHF data transmission communication system using Orthogonal Frequency Division Multiplexing (OFDM) modulation are worked out in this paper. The achieved data rate, the spectral efficiency and the bit error rate (BER) represent validation parameters on which the results of the analytical and simulation models are evaluated. It is concluded that the application of the digital OFDM modulation in the maritime VHF band may improve the GMDSS system by achieving higher data rates compared to the current terrestri...
Axioms, 2019
The sampling reconstruction theory is one of the great areas of the analysis in which Paul Leo Bu... more The sampling reconstruction theory is one of the great areas of the analysis in which Paul Leo Butzer earned longstanding and excellent theoretical results. Thus, we are forced either by earlier exhaustive presentations of his research activity and/or the highly voluminous material to restrict ourselves to a more narrow and precise sub-area in consideration; we discuss here, giving deeper insight, Paul Butzer’s sampling theoretical work with special attention concerning sampling stochastic signals.
Journal of the Korean Mathematical Society, 2010
Multiple discrete Hilbert type inequalities are established in the case of non-homogeneous kernel... more Multiple discrete Hilbert type inequalities are established in the case of non-homogeneous kernel function by means of Laplace integral representation of associated Dirichlet series. Using newly derived integral expressions for the Mordell-Tornheim Zeta function a set of subsequent special cases, interesting by themselves, are obtained as corollaries of the main inequality.
Integral Transforms and Special Functions, 2016
Introducing the discrete probability distribution by means of the Prabhakar (or the threeparamete... more Introducing the discrete probability distribution by means of the Prabhakar (or the threeparameter Mittag-Leffler) function, we establish explicit expressions for raw and factorial moments and also general fractional order moments. Applying an elementary moment inequality we obtain functional upper bounds for the Turánian difference for Prabhakar function. Finally, a Laguerre inequality is proved and functional upper bound has been given for Laguerreian difference for Prabhakar function.
Mathematics, Apr 3, 2023
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
Results in mathematics, Feb 24, 2024
Page 1. 417 DIRECT WEIGHTED LAGRANGE - YEN TYPE INTERPOLATION IN Lt-n,a12 Tihor K. PogAny and Mat... more Page 1. 417 DIRECT WEIGHTED LAGRANGE - YEN TYPE INTERPOLATION IN Lt-n,a12 Tihor K. PogAny and Mato Tudor University of Ri.jeka, Department of Maritime Studies 51000 Rijeka, Studentska 2, Croatia poganj@brod.pfri.hr & tudor@brod.pfri.hr Abstract ...
arXiv (Cornell University), Jun 27, 2016
Motivated by several generalizations of the well-known Mathieu series, the main object of this pa... more Motivated by several generalizations of the well-known Mathieu series, the main object of this paper is to introduce new extension of generalized Mathieu series and to derive various integral representations of such series. Finally master bounding inequality is established using the newly derived integral expression.
arXiv (Cornell University), Apr 12, 2016
This paper is concerned with new results for the circular Eisenstein series εr(z) as well as with... more This paper is concerned with new results for the circular Eisenstein series εr(z) as well as with a novel approach to Hilbert-Eisenstein series hr(z), introduced by Michael Hauss in 1995. The latter turn out to be the product of the hyperbolic sinh-function with an explicit closed form linear combination of digamma functions. The results, which include differentiability properties and integral representations, are established by independent and different argumentations. Highlights are new results on the Butzer-Flocke-Hauss Omega function, one basis for the study of Hilbert-Eisenstein series, which have been the subject of several recent papers.
Integral Transforms and Special Functions, Jun 22, 2016
Introducing the discrete probability distribution by means of the Prabhakar (or the threeparamete... more Introducing the discrete probability distribution by means of the Prabhakar (or the threeparameter Mittag-Leffler) function, we establish explicit expressions for raw and factorial moments and also general fractional order moments. Applying an elementary moment inequality we obtain functional upper bounds for the Turánian difference for Prabhakar function. Finally, a Laguerre inequality is proved and functional upper bound has been given for Laguerreian difference for Prabhakar function.
Mathematics, Aug 29, 2022
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
Anais Da Academia Brasileira De Ciencias, Jun 1, 2010
The five parameter gamma-Weibull distribution has been introduced by Leipnik and Pearce (2004). N... more The five parameter gamma-Weibull distribution has been introduced by Leipnik and Pearce (2004). Nadarajah and Kotz (2007) have simplified it into four parameter form, using hypergeometric functions in some special cases. We show that the probability distribution function, all moments of positive order and the characteristic function of gamma-Weibull distribution of a random variable can be explicitely expressed in terms of the incomplete confluent Fox-Wright Psi-function, which is recently introduced by Srivastava and Pogány (2007). In the same time, we generalize certain results by Nadarajah and Kotz that follow as special cases of our findings.
Tbilisi Mathematical Journal, 2014
This paper deals with the derivation of certain new Pólya-Szegő type inequalities by making use o... more This paper deals with the derivation of certain new Pólya-Szegő type inequalities by making use of the Saigo fractional integral operator. The results obtained cover the same kind of conclusions in the case of Riemann-Liouville and Erdélyi-Kober fractional integral operators.
Applied Mathematics and Computation, Jul 1, 2021
Mathematics
We establish several new functional bounds and uniform bounds (with respect to the variable) for ... more We establish several new functional bounds and uniform bounds (with respect to the variable) for the lower incomplete generalized Fox–Wright functions by means of the representation formulae for the McKay Iν Bessel probability distribution’s cumulative distribution function. New cumulative distribution functions are generated and expressed in terms of lower incomplete Fox–Wright functions and/or generalized hypergeometric functions, whilst in the closing part of the article, related bounding inequalities are obtained for them.
Journal of Mathematical Inequalities
A new generalization of Whittaker function M λ ,μ (z) is introduced and studied by means of the e... more A new generalization of Whittaker function M λ ,μ (z) is introduced and studied by means of the extended multi-index confluent hypergeometric function of the first kind Φ (γ i),p (α i ,β i) introduced in [1]. The related Euler-type integral representation and the Laplace-Mellin and Hankel integral transforms are also presented. Functional two-sided bounding inequality is established for the multi-index Mittag-Leffler function, and in continuation functional lower bound is derived for the associated ML-extended Whittaker function.
Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), 2017
In this paper, motivated by certain recent extensions of the Euler’s beta, Gauss’ hypergeometric ... more In this paper, motivated by certain recent extensions of the Euler’s beta, Gauss’ hypergeometric and confluent hypergeometric functions (see [4]), we extend the Srivastava’s triple hypergeometric function HA by making use of two additional parameters in the integrand. Systematic investigation of its properties including, among others, various integral representations of Euler and Laplace type, Mellin transforms, Laguerre polynomial representation, transformation formulas and a recurrence relation, is presented. Also, by virtue of Luke’s bounds for hypergeometric functions and various bounds upon the Bessel functions appearing in the kernels of the newly established integral representations, we deduce a set of bounding inequalities for the extended Srivastava’s triple hypergeometric function HA,p,q.
Comptes Rendus Mathematique, 2018
On properties and applications of (p, q)-extended τ-hypergeometric functions Sur les propriétés e... more On properties and applications of (p, q)-extended τ-hypergeometric functions Sur les propriétés et applications des fonctions τ-hypergéométriques
Applicable Analysis and Discrete Mathematics, 2017
In 2000 Chen introduced a two-parameter lifetime model and has reported only a few mathematical p... more In 2000 Chen introduced a two-parameter lifetime model and has reported only a few mathematical properties moments, quantile and generating functions, among others. In this article, we derive a power series expansion for newly introduced real upper parameter generalized integro-exponential function Eps(z) extending certain Milgram's findings. By our novel results we derive closed-form expressions for the moments, generating function, R?nyi entropy and power series for the quantile function of the Chen distribution.
Polish Maritime Research, 2018
In the maritime Very High Frequency (VHF) band, there are no systems for transmitting large amoun... more In the maritime Very High Frequency (VHF) band, there are no systems for transmitting large amounts of data. Therefore, it is necessary to develop new systems that would modernize the Global Maritime Distress and Safety System (GMDSS), significantly relieve the Automatic Identification System’s (AIS) communication channels, and set guidelines for the development of communication infrastructure of the e-Navigation. In line with this, analytical and simulation models of the maritime VHF data transmission communication system using Orthogonal Frequency Division Multiplexing (OFDM) modulation are worked out in this paper. The achieved data rate, the spectral efficiency and the bit error rate (BER) represent validation parameters on which the results of the analytical and simulation models are evaluated. It is concluded that the application of the digital OFDM modulation in the maritime VHF band may improve the GMDSS system by achieving higher data rates compared to the current terrestri...
Axioms, 2019
The sampling reconstruction theory is one of the great areas of the analysis in which Paul Leo Bu... more The sampling reconstruction theory is one of the great areas of the analysis in which Paul Leo Butzer earned longstanding and excellent theoretical results. Thus, we are forced either by earlier exhaustive presentations of his research activity and/or the highly voluminous material to restrict ourselves to a more narrow and precise sub-area in consideration; we discuss here, giving deeper insight, Paul Butzer’s sampling theoretical work with special attention concerning sampling stochastic signals.
Journal of the Korean Mathematical Society, 2010
Multiple discrete Hilbert type inequalities are established in the case of non-homogeneous kernel... more Multiple discrete Hilbert type inequalities are established in the case of non-homogeneous kernel function by means of Laplace integral representation of associated Dirichlet series. Using newly derived integral expressions for the Mordell-Tornheim Zeta function a set of subsequent special cases, interesting by themselves, are obtained as corollaries of the main inequality.
Integral Transforms and Special Functions, 2016
Introducing the discrete probability distribution by means of the Prabhakar (or the threeparamete... more Introducing the discrete probability distribution by means of the Prabhakar (or the threeparameter Mittag-Leffler) function, we establish explicit expressions for raw and factorial moments and also general fractional order moments. Applying an elementary moment inequality we obtain functional upper bounds for the Turánian difference for Prabhakar function. Finally, a Laguerre inequality is proved and functional upper bound has been given for Laguerreian difference for Prabhakar function.