Abstract
References
- [1] G.E. Andrews, R. Askey and R. Roy, Special functions, Cambridge University Press, Cambridge, 1999.
- [2] M.A. Chaudhry and S.M. Zubair, Generalized incomplete gamma functions with applications, J. Comput. Appl. Math. 55, 99–124, 1994.
- [3] M.A. Chaudhry, A. Qadir, M. Rafique and S.M. Zubair, Extension of Euler’s beta function, J. Comput. Appl. Math. 78, 19–32, 1997.
- [4] M.A. Chaudhry, A. Qadir, H.M. Srivastava and R.B. Paris, Extended Hypergeometric and Confluent Hypergeometric functions, Appl. Math. Comput. 159, 589–602, 2004.
- [5] J. Choi, A.K Rathie and R.K. Parmar, Extension of extended beta , hypergeometric and confluent hypergeometric functions, Honam Math. J. 36 (2), 357–385, 2014.
- [6] R. Gorenflo, A.A. Kilbas, F. Mainardi and S.V. Rogosin, Mittag-Leffler Functions, Related Topics and Applications, Springer, 2014.
- [7] M. Ghayasuddin and N.U. Khan, Remarks on extended Gauss hypergeometric functions, Acta Universitatis Apulensis 49, 1–13, 2017.
- [8] N.U. Khan and S. Husain, A note on extended beta function inolving generalized Mittag-Leffler function and its applications, TWMS J. Appl. Eng. Math. 12 (1), 71- 81, 2022.
- [9] N.U. Khan, S. Husain, T. Usman and S. Araci, Results Concerning the Analysis of Multi-Index Whittaker Function, Journal of Mathematics Vol. 2022, Article ID 3828104, 2022. https://doi.org/10.1155/2022/3828104
- [10] N.U. Khan, T. Usman and M. Aman, Extended Beta, Hypergeometric and confluent Hypergeometric functions, Transactions issues Mathematics series of physicaltechnical Mathematics science Azerbaijan National Academy of Science 39(1), 83–97, 2019.
- [11] N.U. Khan, T. Usman and M. Aman, Extended Beta, Hypergeometric and Confluent Hypergeometric Functions Via Multi-index Mittag-Leffler Function, Proceedings of the Jangjeon Mathematical Society 25 (1), 43-58, 2022.
- [12] E. Özerjin, M.A. Özarslan and A. Altin, Extension of gamma, beta and hypergeometric functions, J. Comput. Appl. Math. 235, 4601–4610, 2011.
- [13] M. Raïssouli and M. Chergui, On a new parametrized Beta functions, Proceedings of the Institute of Mathematics and Mechanics National Academy of Sciences of Azerbaijan 48 (1), 2022.
- [14] A. Wiman, Uber den fundamental Satz in der Theorie der Funktionen $E_{\aleph}(z)$, Acta Math. 29, 191-201, 1905.
Abstract
The main objective is to introduce a novel kind of beta function known as the beta logarithmic function using extended beta functions and logarithmic mean. Further, we study its essential properties and investigate various formulas of beta logarithmic functions such as integral representation, summation formula, transform formula and their statistical properties. Based on this concept, we introduce new hypergeometric and confluent hypergeometric functions and study their properties.
Keywords
logarithmic mean beta function hypergeometric function confluent hypergeometric function beta distribution
References
- [1] G.E. Andrews, R. Askey and R. Roy, Special functions, Cambridge University Press, Cambridge, 1999.
- [2] M.A. Chaudhry and S.M. Zubair, Generalized incomplete gamma functions with applications, J. Comput. Appl. Math. 55, 99–124, 1994.
- [3] M.A. Chaudhry, A. Qadir, M. Rafique and S.M. Zubair, Extension of Euler’s beta function, J. Comput. Appl. Math. 78, 19–32, 1997.
- [4] M.A. Chaudhry, A. Qadir, H.M. Srivastava and R.B. Paris, Extended Hypergeometric and Confluent Hypergeometric functions, Appl. Math. Comput. 159, 589–602, 2004.
- [5] J. Choi, A.K Rathie and R.K. Parmar, Extension of extended beta , hypergeometric and confluent hypergeometric functions, Honam Math. J. 36 (2), 357–385, 2014.
- [6] R. Gorenflo, A.A. Kilbas, F. Mainardi and S.V. Rogosin, Mittag-Leffler Functions, Related Topics and Applications, Springer, 2014.
- [7] M. Ghayasuddin and N.U. Khan, Remarks on extended Gauss hypergeometric functions, Acta Universitatis Apulensis 49, 1–13, 2017.
- [8] N.U. Khan and S. Husain, A note on extended beta function inolving generalized Mittag-Leffler function and its applications, TWMS J. Appl. Eng. Math. 12 (1), 71- 81, 2022.
- [9] N.U. Khan, S. Husain, T. Usman and S. Araci, Results Concerning the Analysis of Multi-Index Whittaker Function, Journal of Mathematics Vol. 2022, Article ID 3828104, 2022. https://doi.org/10.1155/2022/3828104
- [10] N.U. Khan, T. Usman and M. Aman, Extended Beta, Hypergeometric and confluent Hypergeometric functions, Transactions issues Mathematics series of physicaltechnical Mathematics science Azerbaijan National Academy of Science 39(1), 83–97, 2019.
- [11] N.U. Khan, T. Usman and M. Aman, Extended Beta, Hypergeometric and Confluent Hypergeometric Functions Via Multi-index Mittag-Leffler Function, Proceedings of the Jangjeon Mathematical Society 25 (1), 43-58, 2022.
- [12] E. Özerjin, M.A. Özarslan and A. Altin, Extension of gamma, beta and hypergeometric functions, J. Comput. Appl. Math. 235, 4601–4610, 2011.
- [13] M. Raïssouli and M. Chergui, On a new parametrized Beta functions, Proceedings of the Institute of Mathematics and Mechanics National Academy of Sciences of Azerbaijan 48 (1), 2022.
- [14] A. Wiman, Uber den fundamental Satz in der Theorie der Funktionen $E_{\aleph}(z)$, Acta Math. 29, 191-201, 1905.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | August 15, 2023 |
| Published in Issue | Year 2023 Volume: 52 Issue: 4 |