<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, we introduce a new generalization of the Pochhammer symbol by means of the generalization of extended gamma function <xref ref-type="disp-formula" rid="j_amns.2020.1.00023_eq_004_w2aab3b7e1462b1b6b1ab1ab3c51Aa">(4)</xref>. Using the generalization of Pochhammer symbol, we give a generalization of the extended hypergeo-metric functions one or several variables. Also, we obtain various integral representations, derivative formulas and certain properties of these functions.</p></abstract>

In this paper, we introduce a new generalization of the Pochhammer symbol by means of the generalization of extended gamma function (4). Using the generalization of Pochhammer symbol, we give a generalization of the extended hypergeo-metric functions one or several variables. Also, we obtain various integral representations, derivative formulas and certain properties of these functions.

A New Generalization of Pochhammer Symbol and Its Applications

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"A New Generalization of Pochhammer Symbol and Its Applications"}

In this paper, we introduce a new generalization of the Pochhammer symbol by means of the generalization of extended gamma function (4). Using the...

A New Generalization of Pochhammer Symbol and Its Applications

Published Online: Mar 31, 2020

Page range: 255 - 266

Received: Jun 14, 2019

Accepted: Jul 10, 2019

DOI: https://doi.org/10.2478/amns.2020.1.00023

Keywords
gamma function, beta function, Pochhammer symbol, Gauss hypergeometric function, confluent hypergeometric function, Appell hypergeometric functions, Humbert hypergeometric functions of two variables, integral representations, derivative formulas, recurrence relation

© 2020 Recep Şahin et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

A New Generalization of Pochhammer Symbol and Its Applications

Published Online: Mar 31, 2020

Page range: 255 - 266

Received: Jun 14, 2019

Accepted: Jul 10, 2019

DOI: https://doi.org/10.2478/amns.2020.1.00023

Keywordsgamma function, beta function, Pochhammer symbol, Gauss hypergeometric function, confluent hypergeometric function, Appell hypergeometric functions, Humbert hypergeometric functions of two variables, integral representations, derivative formulas, recurrence relation

© 2020 Recep Şahin et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
gamma function, beta function, Pochhammer symbol, Gauss hypergeometric function, confluent hypergeometric function, Appell hypergeometric functions, Humbert hypergeometric functions of two variables, integral representations, derivative formulas, recurrence relation