The Experts below are selected from a list of 288 Experts worldwide ranked by ideXlab platform
Thabet Abdeljawad - One of the best experts on this subject based on the ideXlab platform.
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properties and applications of a new extended gamma Function involving Confluent Hypergeometric Function
Journal of Mathematics, 2021Co-Authors: Abdus Saboor, Kottakkaran Sooppy Nisar, Gauhar Rahman, Hazrat Ali, Thabet AbdeljawadAbstract:In this paper, a new Confluent Hypergeometric gamma Function and an associated Confluent Hypergeometric Pochhammer symbol are introduced. We discuss some properties, for instance, their different integral representations, derivative formulas, and generating Function relations. Different special cases are also considered.
Abdus Saboor - One of the best experts on this subject based on the ideXlab platform.
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properties and applications of a new extended gamma Function involving Confluent Hypergeometric Function
Journal of Mathematics, 2021Co-Authors: Abdus Saboor, Kottakkaran Sooppy Nisar, Gauhar Rahman, Hazrat Ali, Thabet AbdeljawadAbstract:In this paper, a new Confluent Hypergeometric gamma Function and an associated Confluent Hypergeometric Pochhammer symbol are introduced. We discuss some properties, for instance, their different integral representations, derivative formulas, and generating Function relations. Different special cases are also considered.
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the moment generating Function of a bivariate gamma type distribution
Applied Mathematics and Computation, 2012Co-Authors: Abdus Saboor, Serge B. Provost, Munir AhmadAbstract:A bivariate gamma-type density Function involving a Confluent Hypergeometric Function of two variables is being introduced. The inverse Mellin transform technique is employed in conjunction with the transformation of variable technique to obtain its moment generating Function, which is expressed in terms of generalized Hypergeometric Functions. Its cumulative distribution Function is given in closed form as well. Many distributions such as the bivariate Weibull, Rayleigh, half-normal and Maxwell distributions can be obtained as limiting cases of the proposed gamma-type density Function. Computable representations of the moment generating Functions of these distributions are also provided.
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a bivariate gamma type probability Function using a Confluent Hypergeometric Function of two variables
2012Co-Authors: Abdus Saboor, Munir AhmadAbstract:Al-Saqabi et al. [4] defined a univariate gamma-type Function involving the Confluent hypergeometirc Function of two variables and discussed some associated statistical Functions. We define a bivariate extension of their gamma-type Function using another form of a Confluent Hypergeometric Function of two variables and discuss some of its statistical Functions.
R. K. Saxena - One of the best experts on this subject based on the ideXlab platform.
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generalized gamma type Functions involving kummer s Confluent Hypergeometric Function and associated probability distributions
Integral Transforms and Special Functions, 2007Co-Authors: R. K. Saxena, Chena Ram, Naresh Dudi, S L KallaAbstract:The object of this paper is to define and study a new generalization of the generalized gamma-type Function in the form where Φ (α, β; z) is the well known Kummer’s Confluent Hypergeometric Function and 2 R 1 (·) is a special case of Wright’s generalized Hypergeometric Function. This generalization provides unification and extension of the various generalizations given earlier by Kobayashi, Al-Musallam and Kalla and Virchenko et al. Incomplete generalized gamma Function corresponding to the above defined generalized gamma Function are also defined and their basic properties are investigated, which extend the existing results in the field of generalized gamma-type Functions. We study a class of probability density Functions involving Kummer’s Confluent Hypergeometric Function and 2 R 1 (·).
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Generalized gamma-type Functions involving Kummer’s Confluent Hypergeometric Function and associated probability distributions
Integral Transforms and Special Functions, 2007Co-Authors: R. K. Saxena, Chena Ram, Naresh Dudi, Shyam L. KallaAbstract:The object of this paper is to define and study a new generalization of the generalized gamma-type Function in the form where Φ (α, β; z) is the well known Kummer’s Confluent Hypergeometric Function and 2 R 1 (·) is a special case of Wright’s generalized Hypergeometric Function. This generalization provides unification and extension of the various generalizations given earlier by Kobayashi, Al-Musallam and Kalla and Virchenko et al. Incomplete generalized gamma Function corresponding to the above defined generalized gamma Function are also defined and their basic properties are investigated, which extend the existing results in the field of generalized gamma-type Functions. We study a class of probability density Functions involving Kummer’s Confluent Hypergeometric Function and 2 R 1 (·).
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SOLUTION OF VOLTERRA-TYPE INTEGRO-DIFFERENTIAL EQUATIONS WITH A GENERALIZED LAURICELLA Confluent Hypergeometric Function IN THE KERNELS
International Journal of Mathematics and Mathematical Sciences, 2005Co-Authors: R. K. Saxena, Shyam L. KallaAbstract:The object of this paper is to solve a fractional integro-differential equation involving a generalized Lauricella Confluent Hypergeometric Function in several complex variables and the free term contains a continuous Function f(τ). The method is based on certain properties of fractional calculus and the classical Laplace transform. A Cauchy-type problem involving the Caputo fractional derivatives and a generalized Volterra integral equation are also considered. Several special cases are mentioned. A number of results given recently by various authors follow as particular cases of formulas established here.
Shyam L. Kalla - One of the best experts on this subject based on the ideXlab platform.
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Generalized gamma-type Functions involving Kummer’s Confluent Hypergeometric Function and associated probability distributions
Integral Transforms and Special Functions, 2007Co-Authors: R. K. Saxena, Chena Ram, Naresh Dudi, Shyam L. KallaAbstract:The object of this paper is to define and study a new generalization of the generalized gamma-type Function in the form where Φ (α, β; z) is the well known Kummer’s Confluent Hypergeometric Function and 2 R 1 (·) is a special case of Wright’s generalized Hypergeometric Function. This generalization provides unification and extension of the various generalizations given earlier by Kobayashi, Al-Musallam and Kalla and Virchenko et al. Incomplete generalized gamma Function corresponding to the above defined generalized gamma Function are also defined and their basic properties are investigated, which extend the existing results in the field of generalized gamma-type Functions. We study a class of probability density Functions involving Kummer’s Confluent Hypergeometric Function and 2 R 1 (·).
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SOLUTION OF VOLTERRA-TYPE INTEGRO-DIFFERENTIAL EQUATIONS WITH A GENERALIZED LAURICELLA Confluent Hypergeometric Function IN THE KERNELS
International Journal of Mathematics and Mathematical Sciences, 2005Co-Authors: R. K. Saxena, Shyam L. KallaAbstract:The object of this paper is to solve a fractional integro-differential equation involving a generalized Lauricella Confluent Hypergeometric Function in several complex variables and the free term contains a continuous Function f(τ). The method is based on certain properties of fractional calculus and the classical Laplace transform. A Cauchy-type problem involving the Caputo fractional derivatives and a generalized Volterra integral equation are also considered. Several special cases are mentioned. A number of results given recently by various authors follow as particular cases of formulas established here.
Alexandru Zaharescu - One of the best experts on this subject based on the ideXlab platform.
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zeros of combinations of the riemann ξ Function and the Confluent Hypergeometric Function on bounded vertical shifts
Journal of Mathematical Analysis and Applications, 2018Co-Authors: Atul Dixit, Rahul Kumar, Bibekananda Maji, Alexandru ZaharescuAbstract:Abstract In 1914, Hardy proved that infinitely many non-trivial zeros of the Riemann zeta Function lie on the critical line using the transformation formula of the Jacobi theta Function. Recently the first author obtained an integral representation involving the Riemann Ξ-Function and the Confluent Hypergeometric Function linked to the general theta transformation. Using this result, we show that a series consisting of bounded vertical shifts of a product of the Riemann Ξ-Function and the real part of a Confluent Hypergeometric Function has infinitely many zeros on the critical line, thereby generalizing a previous result due to the first and the last authors along with Roy and Robles. The latter itself is a generalization of Hardy's theorem.
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zeros of combinations of the riemann xi Function and the Confluent Hypergeometric Function on bounded vertical shifts
arXiv: Number Theory, 2017Co-Authors: Atul Dixit, Rahul Kumar, Bibekananda Maji, Alexandru ZaharescuAbstract:In 1914, Hardy proved that infinitely many non-trivial zeros of the Riemann zeta Function lie on the critical line using the transformation formula of the Jacobi theta Function. Recently the first author obtained an integral representation involving the Riemann $\Xi$-Function and the Confluent Hypergeometric Function linked to the general theta transformation. Using this result, we show that a series consisting of bounded vertical shifts of a product of the Riemann $\Xi$-Function and the real part of a Confluent Hypergeometric Function has infinitely many zeros on the critical line, thereby generalizing a previous result due to the first and the last authors along with Roy and Robles. The latter itself is a generalization of Hardy's theorem.