Abstract
Many authors defined and extended the beta function in various forms because the beta function has wide uses in different fields of science and applied science. In this article, we define a new more generalized form of the extended beta matrix function via the Wiman matrix function and describe their significant properties and special cases. Furthermore, we define an extension of the Gauss hypergeometric and confluent hypergeometric matrix functions by adopting a novel type of beta matrix function. We also derive their Laplace transform, derivative formula and transformation formulae.
References
[1] M. Abdalla and A. Bakhet, Extension of Beta matrix function, Asian J. Math. Comput. Res. 9 (2016), 253–264. Search in Google Scholar
[2] M. Abdalla and A. Bakhet, Extended Gauss hypergeometric matrix functions, Iran. J. Sci. Technol. Trans. A Sci. 42 (2018), no. 3, 1465–1470. 10.1007/s40995-017-0183-3Search in Google Scholar
[3] B. Çekim, Generalized Euler’s beta matrix and related functions, AIP Conf. Proc. 1558 (2013), 1132–1135. 10.1063/1.4825707Search in Google Scholar
[4] M. A. Chaudhry, A. Qadir, M. Rafique and S. M. Zubair, Extension of Euler’s beta function, J. Comput. Appl. Math. 78 (1997), no. 1, 19–32. 10.1016/S0377-0427(96)00102-1Search in Google Scholar
[5] M. A. Chaudhry, A. Qadir, H. M. Srivastava and R. B. Paris, Extended hypergeometric and confluent hypergeometric functions, Appl. Math. Comput. 159 (2004), no. 2, 589–602. 10.1016/j.amc.2003.09.017Search in Google Scholar
[6] J. Choi, A. K. Rathie and R. K. Parmar, Extension of extended beta, hypergeometric and confluent hypergeometric functions, Honam Math. J. 36 (2014), no. 2, 357–385. 10.5831/HMJ.2014.36.2.357Search in Google Scholar
[7] L. Debnath and D. Bhatta, Integral Transforms and Their Applications, Chapman & Hall/CRC, Boca Raton, 2016. 10.1201/9781420010916Search in Google Scholar
[8] N. Dunford and J. Schwartz, Linear Operators. Part 1, Interscience, New York, 1963. Search in Google Scholar
[9] G. B. Folland, Fourier Analysis and its Applications, American Mathematical Society, Providence, 2009. Search in Google Scholar
[10] R. Garrappa and M. Popolizio, Computing the matrix Mittag-Leffler function with applications to fractional calculus, J. Sci. Comput. 77 (2018), no. 1, 129–153. 10.1007/s10915-018-0699-5Search in Google Scholar
[11] R. Goyal, P. Agarwal, G. I. Oros and S. Jain, Extended beta and gamma matrix functions via 2-parameter Mittag-Leffler matrix function, Mathematics 10 (2022), no. 6, Paper No. 892. 10.3390/math10060892Search in Google Scholar
[12] S. Jain, R. Goyal, G. I. Oros, P. Agarwal and S. Momani, A study of generalized hypergeometric matrix functions via two-parameter Mittag-Leffler matrix function, Open Phys. 20 (2022), 730–739. 10.1515/phys-2022-0068Search in Google Scholar
[13] L. Jódar and J. C. Cortés, On the hypergeometric matrix function, J. Comput. Appl. Math. 99 (1998), no. 1–2, 205–217. 10.1016/S0377-0427(98)00158-7Search in Google Scholar
[14] L. Jódar and J. C. Cortés, Some properties of gamma and beta matrix functions, Appl. Math. Lett. 11 (1998), no. 1, 89–93. 10.1016/S0893-9659(97)00139-0Search in Google Scholar
[15] 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 (2022), 71–81. Search in Google Scholar
[16] A. Verma, S. Bajpai and K. S. Yadav, Some results of new extended beta, hypergeometric, Appell and Lauricella matrix functions, Res. Math. 9 (2022), no. 1, Paper No. 2151555. 10.1080/27684830.2022.2151555Search in Google Scholar
© 2023 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- On a weak maximum principle for a class of fractional diffusive equations
- On a new class of two-variable functional equations on semigroups with involutions
- Universal lower bound of the convergence rate of solutions for a semi-linear heat equation with a critical exponent
- A novel Beta matrix function via Wiman matrix function and their applications
- Error analysis of approximate operators for a particle method based on Voronoi diagram
Articles in the same Issue
- Frontmatter
- On a weak maximum principle for a class of fractional diffusive equations
- On a new class of two-variable functional equations on semigroups with involutions
- Universal lower bound of the convergence rate of solutions for a semi-linear heat equation with a critical exponent
- A novel Beta matrix function via Wiman matrix function and their applications
- Error analysis of approximate operators for a particle method based on Voronoi diagram