Euler-type integrals for the generalized hypergeometric matrix function

• Autorzy: Pal Ankit , Kumari Kiran

Identyfikatory

DOI

10.1515/jaa-2023-0028

• Języki publikacji: EN

Abstrakty

EN

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 |z| = 1. Recently, hypergeometric matrix functions and their potential applications have played a major role in mathematical physics and engineering. Motivated by aforesaid works and in order to enrich this flourishing field, we investigate the Euler-type integral representations for the generalized hypergeometric matrix function and determine various transformations in terms of hypergeometric matrix functions. Furthermore, unit and half arguments have been provided for several particular cases.

Słowa kluczowe

EN

generalized hypergeometric matrix function; matrix functional calculus; gamma and beta matrix function

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2023
• Tom: Vol. 29, nr 2
• Strony: 359--366
• Opis fizyczny: Bibliogr. 28 poz.

Twórcy

autor

Pal Ankit

• Division of Mathematics, School of Advanced Sciences & Languages, VIT Bhopal University, Kothrikalan, Sehore-466114, Madhya Pradesh, India

• https://orcid.org/0000-0002-5406-630X

autor

Kumari Kiran

• Department of Mathematics, University of Rajasthan, Jaipur-302004, Rajasthan, India

Bibliografia

• [1] M. Abdalla, On the incomplete hypergeometric matrix functions, Ramanujan J. 43 (2017), no. 3, 663-678.
• [2] M. Abdalla, Special matrix functions: Characteristics, achievements and future directions, Linear Multilinear Algebra 68 (2020), no. 1, 1-28.
• [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.
• [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.
• [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.
• [6] E. Defez and L. Jódar, Chebyshev matrix polynomials and second order matrix differential equations, Util. Math. 61 (2002), 107-123.
• [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.
• [8] N. Dunford and J. Schwartz, Linear Operators. Part 1, Addison-Wesley, New York, 1957.
• [9] R. Dwivedi and V. Sahai, On the hypergeometric matrix functions of two variables, Linear Multilinear Algebra 66 (2018), no. 9, 1819-1837.
• [10] R. Dwivedi and V. Sahai, On the basic hypergeometric matrix functions of two variables, Linear Multilinear Algebra 67 (2019), no. 1, 1-19.
• [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.
• [12] G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed., Johns Hopkins University, Baltimore, 1996.
• [13] A. T. James, Special functions of matrix and single argument in statistics, in: Theory and Application of Special Functions, Math. Res. Center Univ. Wisconsin Publ. 35, Academic Press, New York (1975), 497-520.
• [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.
• [15] L. Jódar and J. C. Cortés, On the hypergeometric matrix function, J. Comput. Appl. Math. 99 (1998), 205-217.
• [16] L. Jódar and J. C. Cortés, Some properties of gamma and beta matrix functions, Appl. Math. Lett. 11 (1998), no. 1, 89-93.
• [17] L. Jódar and J. Sastre, On Laguerre matrix polynomials, Util. Math. 53 (1998), 37-48.
• [18] T. Kim and D. S. Kim, Degenerate Laplace transform and degenerate gamma function, Russ. J. Math. Phys. 24 (2017), no. 2, 241-248.
• [19] T. Kim and D. S. Kim, Note on the degenerate gamma function, Russ. J. Math. Phys. 27 (2020), no. 3, 352-358.
• [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.
• [21] T. Kim and D. S. Kim, Combinatorial identities involving degenerate harmonic and hyperharmonic numbers, Adv. Appl. Math. 148 (2023), Paper No. 102535.
• [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.
• [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.
• [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.
• [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.
• [26] A. Pal, V. K. Jatav and A. K. Shukla, Matrix analog of the four-parameter Mittag-Leffler function, Math. Methods Appl. Sci. (2023), DOI 10.1002/mma.9363.
• [27] S. Z. Rida, M. Abul-Dahab, M. A. Saleem and M. T. Mohammed, On Humbert matrix function Ψ1(A, B; C, C; z, w) of two complex variables under differential operator, Int. J. Ind. Math. 32 (2010), 167-179.
• [28] J. B. Seaborn, Hypergeometric Functions and their Applications, Texts Appl. Math. 8, Springer, New York, 1991.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).