A Generalized Gamma-Type Functions Involving Confluent Hypergeometric Mittage-Leffler Function and Associated Probability Distributions

Naresh Dudi

doi:doi:10.11648/j.ijtam.20220804.11

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A Generalized Gamma-Type Functions Involving Confluent Hypergeometric Mittage-Leffler Function and Associated Probability Distributions

Naresh Dudi

Published in International Journal of Theoretical and Applied Mathematics (Volume 8, Issue 4)

Received: 23 May 2022 Accepted: 20 June 2022 Published: 21 October 2022

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Abstract

Gamma function is one of the important special functions occurring in many branches of mathematical physics and is investigated in detail in a number of literatures in recent years. The main object of this paper is to present a systematic study of a unification and generalization of the gamma-type functions, which is defined here by means of the confluent hypergeometric Mittage- Leffler function. Motivated essentially by the sources of the applications of the Mittage-Leffler functions in many areas of science and engineering, the author present in a unified manner. During the last two decades Mittage – Leffler function has come into prominence after about nine decades of its discovery by a Swedish Mathematician Mittage-Leffler, due to the vast potential of this applications in solving the problems of physical, biological, engineering, and earth sciences. In this article we investigated a probability density function associated with the generalized gamma-type function, together with several other related results in the theory of probability and statistics, are also considered.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 8, Issue 4)
DOI	10.11648/j.ijtam.20220804.11
Page(s)	78-84
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2022. Published by Science Publishing Group

Keywords

Special Function, Gamma and Incomplete Gamma Functions, Confluent Hypergeometric Mittage-Leffler Function, Probability Density Function, Moment Generating Function

References

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APA Style

Naresh Dudi. (2022). A Generalized Gamma-Type Functions Involving Confluent Hypergeometric Mittage-Leffler Function and Associated Probability Distributions. International Journal of Theoretical and Applied Mathematics, 8(4), 78-84. https://doi.org/10.11648/j.ijtam.20220804.11

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ACS Style

Naresh Dudi. A Generalized Gamma-Type Functions Involving Confluent Hypergeometric Mittage-Leffler Function and Associated Probability Distributions. Int. J. Theor. Appl. Math. 2022, 8(4), 78-84. doi: 10.11648/j.ijtam.20220804.11

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AMA Style

Naresh Dudi. A Generalized Gamma-Type Functions Involving Confluent Hypergeometric Mittage-Leffler Function and Associated Probability Distributions. Int J Theor Appl Math. 2022;8(4):78-84. doi: 10.11648/j.ijtam.20220804.11

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@article{10.11648/j.ijtam.20220804.11,
  author = {Naresh Dudi},
  title = {A Generalized Gamma-Type Functions Involving Confluent Hypergeometric Mittage-Leffler Function and Associated Probability Distributions},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {8},
  number = {4},
  pages = {78-84},
  doi = {10.11648/j.ijtam.20220804.11},
  url = {https://doi.org/10.11648/j.ijtam.20220804.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20220804.11},
  abstract = {Gamma function is one of the important special functions occurring in many branches of mathematical physics and is investigated in detail in a number of literatures in recent years. The main object of this paper is to present a systematic study of a unification and generalization of the gamma-type functions, which is defined here by means of the confluent hypergeometric Mittage- Leffler function. Motivated essentially by the sources of the applications of the Mittage-Leffler functions in many areas of science and engineering, the author present in a unified manner. During the last two decades Mittage – Leffler function has come into prominence after about nine decades of its discovery by a Swedish Mathematician Mittage-Leffler, due to the vast potential of this applications in solving the problems of physical, biological, engineering, and earth sciences. In this article we investigated a probability density function associated with the generalized gamma-type function, together with several other related results in the theory of probability and statistics, are also considered.},
 year = {2022}
}

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TY  - JOUR
T1  - A Generalized Gamma-Type Functions Involving Confluent Hypergeometric Mittage-Leffler Function and Associated Probability Distributions
AU  - Naresh Dudi
Y1  - 2022/10/21
PY  - 2022
N1  - https://doi.org/10.11648/j.ijtam.20220804.11
DO  - 10.11648/j.ijtam.20220804.11
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 78
EP  - 84
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20220804.11
AB  - Gamma function is one of the important special functions occurring in many branches of mathematical physics and is investigated in detail in a number of literatures in recent years. The main object of this paper is to present a systematic study of a unification and generalization of the gamma-type functions, which is defined here by means of the confluent hypergeometric Mittage- Leffler function. Motivated essentially by the sources of the applications of the Mittage-Leffler functions in many areas of science and engineering, the author present in a unified manner. During the last two decades Mittage – Leffler function has come into prominence after about nine decades of its discovery by a Swedish Mathematician Mittage-Leffler, due to the vast potential of this applications in solving the problems of physical, biological, engineering, and earth sciences. In this article we investigated a probability density function associated with the generalized gamma-type function, together with several other related results in the theory of probability and statistics, are also considered.
VL  - 8
IS  - 4
ER  -

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Author Information

Naresh Dudi

Department of Mathematics and Statistics, Jai Narain Vyas University, Jodhur, India

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APA Style

Naresh Dudi. (2022). A Generalized Gamma-Type Functions Involving Confluent Hypergeometric Mittage-Leffler Function and Associated Probability Distributions. International Journal of Theoretical and Applied Mathematics, 8(4), 78-84. https://doi.org/10.11648/j.ijtam.20220804.11

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ACS Style

Naresh Dudi. A Generalized Gamma-Type Functions Involving Confluent Hypergeometric Mittage-Leffler Function and Associated Probability Distributions. Int. J. Theor. Appl. Math. 2022, 8(4), 78-84. doi: 10.11648/j.ijtam.20220804.11

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AMA Style

Naresh Dudi. A Generalized Gamma-Type Functions Involving Confluent Hypergeometric Mittage-Leffler Function and Associated Probability Distributions. Int J Theor Appl Math. 2022;8(4):78-84. doi: 10.11648/j.ijtam.20220804.11

Copy | Download

@article{10.11648/j.ijtam.20220804.11,
  author = {Naresh Dudi},
  title = {A Generalized Gamma-Type Functions Involving Confluent Hypergeometric Mittage-Leffler Function and Associated Probability Distributions},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {8},
  number = {4},
  pages = {78-84},
  doi = {10.11648/j.ijtam.20220804.11},
  url = {https://doi.org/10.11648/j.ijtam.20220804.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20220804.11},
  abstract = {Gamma function is one of the important special functions occurring in many branches of mathematical physics and is investigated in detail in a number of literatures in recent years. The main object of this paper is to present a systematic study of a unification and generalization of the gamma-type functions, which is defined here by means of the confluent hypergeometric Mittage- Leffler function. Motivated essentially by the sources of the applications of the Mittage-Leffler functions in many areas of science and engineering, the author present in a unified manner. During the last two decades Mittage – Leffler function has come into prominence after about nine decades of its discovery by a Swedish Mathematician Mittage-Leffler, due to the vast potential of this applications in solving the problems of physical, biological, engineering, and earth sciences. In this article we investigated a probability density function associated with the generalized gamma-type function, together with several other related results in the theory of probability and statistics, are also considered.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - A Generalized Gamma-Type Functions Involving Confluent Hypergeometric Mittage-Leffler Function and Associated Probability Distributions
AU  - Naresh Dudi
Y1  - 2022/10/21
PY  - 2022
N1  - https://doi.org/10.11648/j.ijtam.20220804.11
DO  - 10.11648/j.ijtam.20220804.11
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 78
EP  - 84
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20220804.11
AB  - Gamma function is one of the important special functions occurring in many branches of mathematical physics and is investigated in detail in a number of literatures in recent years. The main object of this paper is to present a systematic study of a unification and generalization of the gamma-type functions, which is defined here by means of the confluent hypergeometric Mittage- Leffler function. Motivated essentially by the sources of the applications of the Mittage-Leffler functions in many areas of science and engineering, the author present in a unified manner. During the last two decades Mittage – Leffler function has come into prominence after about nine decades of its discovery by a Swedish Mathematician Mittage-Leffler, due to the vast potential of this applications in solving the problems of physical, biological, engineering, and earth sciences. In this article we investigated a probability density function associated with the generalized gamma-type function, together with several other related results in the theory of probability and statistics, are also considered.
VL  - 8
IS  - 4
ER  -

Copy | Download