On certain properties of some generalized special functions
DOI:
https://doi.org/10.4067/S0716-09172003000100005Keywords:
Generalized Special Functions, Lie Algebra.Abstract
In this paper, we derive a result concerning eigenvector for the product of two operators defined on a Lie algebra of endomorphisms of a vector space. The results given by Radulescu, Mandal and authors follow as special cases of this result. Further using these results, we deduce certain properties of generalized Hermite polynomials and Hermite Tricomi functions.
References
[1] G. Dattoli and A. Torre; Theory and Applications of Generalized Bessel Functions, ARACNE, Rome (1996).
[2] G. Dattoli, A. Torre and M. Carpanese; Operational rules and arbitrary order Hermite generating functions, J. Math. Anal. Appl., 227, pp. 98-111, (1998).
[3] G. Dattoli and A. Torre; Operational methods and two variable Laguerre polynomials, Acc. Sc. Torino-Atti Sc. Fis., 132, pp. 1-7, (1998).
[4] G. Dattoli and A. Torre; Exponential operators, quasi-monomials and generalized polynomials, Radiation Physics and Chemistry, 57, pp. 21-26, (2000).
[5] H. L. Krall and O. Frink; A new class of orthogonal polynomials: the Bessel polynomials, Trans. Amer. Math. Soc., 65, pp. 100-115, (1949).
[6] A. K. Mandal; Some operators on a Lie algebra and simple Bessel polynomials, Soochow J. Math., 25, No. 3, pp. 273-276, (1999).
[7] M. A. Pathan and Subuhi Khan; Some properties of two variable Laguerre polynomials via Lie algebra, To appear in Integral Transforms and Special Functions, (2002-2003).
[8] V. D. Radulescu; A study of some special functions with Lie theory, Stud. Cerc. Mat., 43, No. 1-2, pp. 67-71, (1991).
[9] H. M. Srivastava and H. L. Manocha; A Treatise on Generating Functions, Ellis Horwood Limited, Chichester, New York, (1984).
[2] G. Dattoli, A. Torre and M. Carpanese; Operational rules and arbitrary order Hermite generating functions, J. Math. Anal. Appl., 227, pp. 98-111, (1998).
[3] G. Dattoli and A. Torre; Operational methods and two variable Laguerre polynomials, Acc. Sc. Torino-Atti Sc. Fis., 132, pp. 1-7, (1998).
[4] G. Dattoli and A. Torre; Exponential operators, quasi-monomials and generalized polynomials, Radiation Physics and Chemistry, 57, pp. 21-26, (2000).
[5] H. L. Krall and O. Frink; A new class of orthogonal polynomials: the Bessel polynomials, Trans. Amer. Math. Soc., 65, pp. 100-115, (1949).
[6] A. K. Mandal; Some operators on a Lie algebra and simple Bessel polynomials, Soochow J. Math., 25, No. 3, pp. 273-276, (1999).
[7] M. A. Pathan and Subuhi Khan; Some properties of two variable Laguerre polynomials via Lie algebra, To appear in Integral Transforms and Special Functions, (2002-2003).
[8] V. D. Radulescu; A study of some special functions with Lie theory, Stud. Cerc. Mat., 43, No. 1-2, pp. 67-71, (1991).
[9] H. M. Srivastava and H. L. Manocha; A Treatise on Generating Functions, Ellis Horwood Limited, Chichester, New York, (1984).
Published
2017-04-24
How to Cite
[1]
M. A. Pathan and S. Khan, “On certain properties of some generalized special functions”, Proyecciones (Antofagasta, On line), vol. 22, no. 1, pp. 81-89, Apr. 2017.
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