Another method for proving certain reduction formulas for the Humbert function ψ2 due to Brychkov et al. with an application
Recently, Brychkov et al. established several new and interesting reduction formulas for the Humbert functions (the confluent hypergeometric functions of two variables). The primary objective of this study was to provide an alternative and simple approach for proving four reduction formulas for the...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Published: |
Multidisciplinary Digital Publishing Institute
2022
|
| _version_ | 1811137572610506752 |
|---|---|
| author | Mohammed, Asmaa O. Kilicman, Adem Awad, Mohamed M. Rathie, Arjun K. |
| author_facet | Mohammed, Asmaa O. Kilicman, Adem Awad, Mohamed M. Rathie, Arjun K. |
| author_sort | Mohammed, Asmaa O. |
| collection | UPM |
| description | Recently, Brychkov et al. established several new and interesting reduction formulas for the Humbert functions (the confluent hypergeometric functions of two variables). The primary objective of this study was to provide an alternative and simple approach for proving four reduction formulas for the Humbert function ψ2. We construct intriguing series comprising the product of two confluent hypergeometric functions as an application. Numerous intriguing new and previously known outcomes are also achieved as specific instances of our primary discoveries. It is well-known that the hypergeometric functions in one and two variables and their confluent forms occur naturally in a wide variety of problems in applied mathematics, statistics, operations research, physics (theoretical and mathematical) and engineering mathematics, so the results established in this paper may be potentially useful in the above fields. Symmetry arises spontaneously in the above mentioned functions. |
| first_indexed | 2024-09-25T03:36:26Z |
| format | Article |
| id | upm.eprints-100262 |
| institution | Universiti Putra Malaysia |
| last_indexed | 2024-09-25T03:36:26Z |
| publishDate | 2022 |
| publisher | Multidisciplinary Digital Publishing Institute |
| record_format | dspace |
| spelling | upm.eprints-1002622024-07-09T03:24:06Z http://psasir.upm.edu.my/id/eprint/100262/ Another method for proving certain reduction formulas for the Humbert function ψ2 due to Brychkov et al. with an application Mohammed, Asmaa O. Kilicman, Adem Awad, Mohamed M. Rathie, Arjun K. Recently, Brychkov et al. established several new and interesting reduction formulas for the Humbert functions (the confluent hypergeometric functions of two variables). The primary objective of this study was to provide an alternative and simple approach for proving four reduction formulas for the Humbert function ψ2. We construct intriguing series comprising the product of two confluent hypergeometric functions as an application. Numerous intriguing new and previously known outcomes are also achieved as specific instances of our primary discoveries. It is well-known that the hypergeometric functions in one and two variables and their confluent forms occur naturally in a wide variety of problems in applied mathematics, statistics, operations research, physics (theoretical and mathematical) and engineering mathematics, so the results established in this paper may be potentially useful in the above fields. Symmetry arises spontaneously in the above mentioned functions. Multidisciplinary Digital Publishing Institute 2022-04-23 Article PeerReviewed Mohammed, Asmaa O. and Kilicman, Adem and Awad, Mohamed M. and Rathie, Arjun K. (2022) Another method for proving certain reduction formulas for the Humbert function ψ2 due to Brychkov et al. with an application. Symmetry, 14 (5). art. no. 868. pp. 1-14. ISSN 2073-8994 https://www.mdpi.com/2073-8994/14/5/868 10.3390/sym14050868 |
| spellingShingle | Mohammed, Asmaa O. Kilicman, Adem Awad, Mohamed M. Rathie, Arjun K. Another method for proving certain reduction formulas for the Humbert function ψ2 due to Brychkov et al. with an application |
| title | Another method for proving certain reduction formulas for the Humbert function ψ2 due to Brychkov et al. with an application |
| title_full | Another method for proving certain reduction formulas for the Humbert function ψ2 due to Brychkov et al. with an application |
| title_fullStr | Another method for proving certain reduction formulas for the Humbert function ψ2 due to Brychkov et al. with an application |
| title_full_unstemmed | Another method for proving certain reduction formulas for the Humbert function ψ2 due to Brychkov et al. with an application |
| title_short | Another method for proving certain reduction formulas for the Humbert function ψ2 due to Brychkov et al. with an application |
| title_sort | another method for proving certain reduction formulas for the humbert function ψ2 due to brychkov et al with an application |
| work_keys_str_mv | AT mohammedasmaao anothermethodforprovingcertainreductionformulasforthehumbertfunctionps2duetobrychkovetalwithanapplication AT kilicmanadem anothermethodforprovingcertainreductionformulasforthehumbertfunctionps2duetobrychkovetalwithanapplication AT awadmohamedm anothermethodforprovingcertainreductionformulasforthehumbertfunctionps2duetobrychkovetalwithanapplication AT rathiearjunk anothermethodforprovingcertainreductionformulasforthehumbertfunctionps2duetobrychkovetalwithanapplication |