Differential equations for certain hybrid special matrix polynomials
DOI:
https://doi.org/10.5269/bspm.52758Resumen
The main aim of this article is to find the matrix recurrence relation and shift operators for the Gould-Hopper-Laguerre-Appell matrix polynomials. The matrix differential, matrix integro-differential and matrix partial differential equations are derived for these polynomials via factorization method. Certain examples are constructed in order to illustrate the applications of the results.
Referencias
1. Cekim, B. and Aktas, R., Multivariable matrix generalization of Gould-Hopper polynomials, Miskolc Math. Notes 16, 79-89, (2015).
2. Constantine, A. G. and Muirhead, R. J., Partial differential equations for hypergeometric functions of two argument matrix, J. Mult. Anal. 2, 332-338, (1972).
3. He, M. X. and Ricci, P. E., Differential equation of Appell polynomials via the factorization method, J. Comput. Appl. Math. 139, 231-237, (2002).
4. Infeld, L. and Hull, T. E., The factorization method, Rev. Mod. Phys. 23, 21-68, (1951).
5. Khan, S. and Nahid, T., Determinant Forms, Difference Equations and Zeros of the q-Hermite-Appell Polynomials, Mathematics 6, 1-16, (2018).
6. Khan, S. and Nahid, T., Finding non-linear differential equations and certain identities for the Bernoulli-Euler and Bernoulli-Genocchi numbers, SN Appl. Sci. 1, 217, (2019).
7. Nahid, T. and Khan, S., Construction of some hybrid relatives of Laguerre-Appell polynomials associated with GouldHopper matrix polynomials, The J. Anal. 1-20, (2021).
8. Ozarslan, M. A. and Yılmaz, B. Y., A set of finite order differential equations for the Appell polynomials, J. Comput. Appl. Math. 259, 108-116, (2014).
9. Riyasat, M., Khan, S. and Nahid, T., q-difference equations for the composite 2D q-Appell polynomials and their applications, Cogent Mathematics 4: 1376972, (2017).
10. Srivastava, H. M., Ozarslan, M. A. and Yilmaz, B., Some families of differential equations associated with the Hermitebased Appell polynomials and other classes of Hermite-based polynomials, Filomat 28, 695-708, (2014).
11. Terras, A., Special functions for the symmetric space of positive matrices, SIAM J. Math. Anal. 16, 620-640, (1985).
12. Yilmaz, B. and Ozarslan, M. A., Differential equations for the extended 2D Bernoulli and Euler polynomials, Adv. Differ. Equ. 107, 1-16, (2013) .
2. Constantine, A. G. and Muirhead, R. J., Partial differential equations for hypergeometric functions of two argument matrix, J. Mult. Anal. 2, 332-338, (1972).
3. He, M. X. and Ricci, P. E., Differential equation of Appell polynomials via the factorization method, J. Comput. Appl. Math. 139, 231-237, (2002).
4. Infeld, L. and Hull, T. E., The factorization method, Rev. Mod. Phys. 23, 21-68, (1951).
5. Khan, S. and Nahid, T., Determinant Forms, Difference Equations and Zeros of the q-Hermite-Appell Polynomials, Mathematics 6, 1-16, (2018).
6. Khan, S. and Nahid, T., Finding non-linear differential equations and certain identities for the Bernoulli-Euler and Bernoulli-Genocchi numbers, SN Appl. Sci. 1, 217, (2019).
7. Nahid, T. and Khan, S., Construction of some hybrid relatives of Laguerre-Appell polynomials associated with GouldHopper matrix polynomials, The J. Anal. 1-20, (2021).
8. Ozarslan, M. A. and Yılmaz, B. Y., A set of finite order differential equations for the Appell polynomials, J. Comput. Appl. Math. 259, 108-116, (2014).
9. Riyasat, M., Khan, S. and Nahid, T., q-difference equations for the composite 2D q-Appell polynomials and their applications, Cogent Mathematics 4: 1376972, (2017).
10. Srivastava, H. M., Ozarslan, M. A. and Yilmaz, B., Some families of differential equations associated with the Hermitebased Appell polynomials and other classes of Hermite-based polynomials, Filomat 28, 695-708, (2014).
11. Terras, A., Special functions for the symmetric space of positive matrices, SIAM J. Math. Anal. 16, 620-640, (1985).
12. Yilmaz, B. and Ozarslan, M. A., Differential equations for the extended 2D Bernoulli and Euler polynomials, Adv. Differ. Equ. 107, 1-16, (2013) .
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2022-12-24
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