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Some Results on Bicomplex Numbers and Bicomplex Functions

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1Department of Mathematics, Faculty of Science, University of Tabuk, PO Box 4279, Tabuk 71491, Saudi Arabia.2Department of Mathematics, University of Ostrava, Mlynska 702/5, 702 00 Moravska Ostrava, Czechia.3Department of Mathematics, University Center for Research and Development Chandigarh University, Mohali-140243, Punjab, India.

* Corresponding Author: Md. Nasiruzzaman. Email:

Annals of Communications in Mathematics 2025, 8 (2), 303-316. https://doi.org/10.62072/acm.2025.080213

Received: 28 May 2025 |

Accepted: 21 June 2025 |

Published: 30 June 2025

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Abstract

In this paper, we obtain some results on infinite products in bi-complex space, and the exact order of simultaneous results with quantitative estimate for the bi- complex gamma functions and bi-complex Beta functions. Finally using the specific re- sults of complex gamma operator and complex beta operator we introduce the bi-complex gamma functions and bi-complex beta operators and obtain some results.

Keywords

bi-complex Euler’s beta operator; bi-complex Euler’s gamma function; bi-complex holomorphic function; Bi-complex number; infinite product on bi- complex space

Cite This Article

Md. Nasiruzzaman, Mohammad Ayman-mursaleen, Nadeem Rao.

Some Results on Bicomplex Numbers and Bicomplex Functions.

Annals of Communications in Mathematics

2025,

8 (2):

303-316.

https://doi.org/10.62072/acm.2025.080213

Copyright © 2025 by the Author(s). Licensee Techno Sky Publications. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).