Abstract
The special matrix functions have received significant attention in many fields, such as theoretical physics, number theory, probability theory, and the theory of group representations. In 2017, Dwivedi and Sahai introduced the generalized hypergeometric matrix function using matrix parameters and proved the convergence on
Dedicated to my daughter Vamsi Pal on her second birthday
Acknowledgements
The authors would like to thank the referees for their insightful comments and suggestions, which led to a better presentation of the paper.
References
[1] M. Abdalla, On the incomplete hypergeometric matrix functions, Ramanujan J. 43 (2017), no. 3, 663–678. 10.1007/s11139-016-9795-zSuche in Google Scholar
[2] M. Abdalla, Special matrix functions: Characteristics, achievements and future directions, Linear Multilinear Algebra 68 (2020), no. 1, 1–28. 10.1080/03081087.2018.1497585Suche in Google Scholar
[3] M. Akel, A. Bakhet, M. Abdalla and F. He, On degenerate gamma matrix functions and related functions, Linear Multilinear Algebra 71 (2023), no. 4, 673–691. 10.1080/03081087.2022.2040942Suche in Google Scholar
[4] A. G. Constantine and R. J. Muirhead, Partial differential equations for hypergeometric functions of two argument matrices, J. Multivariate Anal. 2 (1972), 332–338. 10.1016/0047-259X(72)90020-6Suche in Google Scholar
[5] J.-C. Cortés, L. Jódar, F. J. Solís and R. Ku-Carrillo, Infinite matrix products and the representation of the matrix gamma function, Abstr. Appl. Anal. 2015 (2015), Article ID 564287. 10.1155/2015/564287Suche in Google Scholar
[6] E. Defez and L. Jódar, Chebyshev matrix polynomials and second order matrix differential equations, Util. Math. 61 (2002), 107–123. Suche in Google Scholar
[7] E. Defez, L. Jódar and A. Law, Jacobi matrix differential equation, polynomial solutions, and their properties, Comput. Math. Appl. 48 (2004), no. 5–6, 789–803. 10.1016/j.camwa.2004.01.011Suche in Google Scholar
[8] N. Dunford and J. Schwartz, Linear Operators. Part 1, Addison-Wesley, New York, 1957. Suche in Google Scholar
[9] R. Dwivedi and V. Sahai, On the hypergeometric matrix functions of two variables, Linear Multilinear Algebra 66 (2018), no. 9, 1819–1837. 10.1080/03081087.2017.1373732Suche in Google Scholar
[10] R. Dwivedi and V. Sahai, On the basic hypergeometric matrix functions of two variables, Linear Multilinear Algebra 67 (2019), no. 1, 1–19. 10.1080/03081087.2017.1406893Suche in Google Scholar
[11] R. Dwivedi and V. Sahai, On certain properties and expansions of zeta matrix function, digamma matrix function and polygamma matrix function, Quaest. Math. 43 (2020), no. 1, 97–105. 10.2989/16073606.2018.1539046Suche in Google Scholar
[12] G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed., Johns Hopkins University, Baltimore, 1996. Suche in Google Scholar
[13] A. T. James, Special functions of matrix and single argument in statistics, Theory and Application of Special Functions, Math. Res. Center Univ. Wisconsin Publ. 35, Academic Press, New York (1975), 497–520. 10.1016/B978-0-12-064850-4.50016-1Suche in Google Scholar
[14] L. Jódar and R. Company, Hermite matrix polynomials and second order matrix differential equations, Approx. Theory Appl. (N. S.) 12 (1996), no. 2, 20–30. 10.1007/BF02836202Suche in Google Scholar
[15] L. Jódar and J. C. Cortés, On the hypergeometric matrix function, J. Comput. Appl. Math. 99 (1998), 205–217. 10.1016/S0377-0427(98)00158-7Suche in Google Scholar
[16] 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)00139-0Suche in Google Scholar
[17] L. Jódar and J. Sastre, On Laguerre matrix polynomials, Util. Math. 53 (1998), 37–48. Suche in Google Scholar
[18] T. Kim and D. S. Kim, Degenerate Laplace transform and degenerate gamma function, Russ. J. Math. Phys. 24 (2017), no. 2, 241–248. 10.1134/S1061920817020091Suche in Google Scholar
[19] T. Kim and D. S. Kim, Note on the degenerate gamma function, Russ. J. Math. Phys. 27 (2020), no. 3, 352–358. 10.1134/S1061920820030061Suche in Google Scholar
[20] T. Kim and D. S. Kim, Some identities on degenerate r-Stirling numbers via boson operators, Russ. J. Math. Phys. 29 (2022), no. 4, 508–517. 10.1134/S1061920822040094Suche in Google Scholar
[21] T. Kim and D. S. Kim, Combinatorial identities involving degenerate harmonic and hyperharmonic numbers, Adv. Appl. Math. 148 (2023), Paper No. 102535. 10.1016/j.aam.2023.102535Suche in Google Scholar
[22] T. Kim, D. S. Kim, L.-C. Jang, H. Lee and H. Kim, Generalized degenerate Bernoulli numbers and polynomials arising from Gauss hypergeometric function, Adv. Difference Equ. 2021 (2021), Paper No. 175. 10.1186/s13662-021-03337-5Suche in Google Scholar
[23] T. Kim, D. S. Kim and H. K. Kim, On generalized degenerate Euler-Genocchi polynomials, Appl. Math. Sci. Eng. 31 (2023), no. 1, Paper No. 2159958. 10.1080/27690911.2022.2159958Suche in Google Scholar
[24] T. Kim, D. S. Kim, H. Lee and J. Kwon, Degenerate binomial coefficients and degenerate hypergeometric functions, Adv. Difference Equ. 2020 (2020), Paper No. 115. 10.1186/s13662-020-02575-3Suche in Google Scholar
[25] Z. M. G. Kishka, A. Shehata and M. Abul-Dahab, On Humbert matrix functions and their properties, Afr. Mat. 24 (2013), no. 4, 615–623. 10.1007/s13370-012-0083-9Suche in Google Scholar
[26] A. Pal, V. K. Jatav and A. K. Shukla, Matrix analog of the four-parameter Mittag–Leffler function, Math. Methods Appl. Sci. (2023), 10.1002/mma.9363. 10.1002/mma.9363Suche in Google Scholar
[27]
S. Z. Rida, M. Abul-Dahab, M. A. Saleem and M. T. Mohammed,
On Humbert matrix function
[28] J. B. Seaborn, Hypergeometric Functions and their Applications, Texts Appl. Math. 8, Springer, New York, 1991. 10.1007/978-1-4757-5443-8Suche in Google Scholar
© 2023 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Around the Świątkowski-type conditions
- Metamorphism—an integral transform reducing the order of a differential equation
- Linear isomorphic spaces of Cesàro–Nörlund operator, their duals and matrix transformations
- A generalized Suzuki–Berinde contraction that characterizes Banach spaces
- Asymptotic behavior of solutions toward the constant state to the Cauchy problem for the non-viscous diffusive dispersive conservation law
- Trigonometric Hermite interpolation method for Fredholm linear integral equations
- Smoothing Levenberg–Marquardt algorithm for solving non-Lipschitz absolute value equations
- Two-dimensional EMD with shape-preserving spline interpolation
- Computing subdifferential limits of operators on Banach spaces
- Certain aspects of ℐ-statistical supremum and ℐ-statistical infimum of real-valued sequences
- Weighted Simpson-like type inequalities for quasi-convex functions
- Bochner formula in generalized (k,μ)-space forms
- Convergence of a conjugate function in Zygmund space by almost Nörlund transform
- 2-point left Radau-type inequalities via s-convexity
- A general size-biased distribution
- A study of fuzzy anti-λ-ideal convergent triple sequence spaces
- Euler-type integrals for the generalized hypergeometric matrix function
- Korn’s inequality in anisotropic Sobolev spaces
Artikel in diesem Heft
- Frontmatter
- Around the Świątkowski-type conditions
- Metamorphism—an integral transform reducing the order of a differential equation
- Linear isomorphic spaces of Cesàro–Nörlund operator, their duals and matrix transformations
- A generalized Suzuki–Berinde contraction that characterizes Banach spaces
- Asymptotic behavior of solutions toward the constant state to the Cauchy problem for the non-viscous diffusive dispersive conservation law
- Trigonometric Hermite interpolation method for Fredholm linear integral equations
- Smoothing Levenberg–Marquardt algorithm for solving non-Lipschitz absolute value equations
- Two-dimensional EMD with shape-preserving spline interpolation
- Computing subdifferential limits of operators on Banach spaces
- Certain aspects of ℐ-statistical supremum and ℐ-statistical infimum of real-valued sequences
- Weighted Simpson-like type inequalities for quasi-convex functions
- Bochner formula in generalized (k,μ)-space forms
- Convergence of a conjugate function in Zygmund space by almost Nörlund transform
- 2-point left Radau-type inequalities via s-convexity
- A general size-biased distribution
- A study of fuzzy anti-λ-ideal convergent triple sequence spaces
- Euler-type integrals for the generalized hypergeometric matrix function
- Korn’s inequality in anisotropic Sobolev spaces