1Universidad Nacional Experimental Francisco de Miranda, Coro, Venezuela. Email: greilyn@hotmail.com
2Universidad del Zulia, Maracaibo, Venezuela. Email: lgalue@hotmail.com
Las funciones especiales son de suma importancia para científicos e ingenieros en muchas de sus aplicaciones, siendo las funciones de Bessel de las más utilizadas debido a que surgen en la solución de ecuaciones diferenciales en matemática, física, química, ingeniería y otras ramas de la ciencia y la tecnología; por esta razón diversos autores han estudiado diferentes generalizaciones de las funciones de Bessel. En este trabajo se presentan teoremas de adición, multiplicación y de Graf para la función de Bessel de dos índices y un parámetro (Jm,n(x;τ)).
Palabras clave: Funciones de Bessel generalizadas, teorema de adición, teorema de multiplicación, teorema de Graf.
The special functions are of utmost importance for scientists and engineers, in many of their applications, being Bessel functions of the most used due that they arise in the solution of differential equations from mathematics, physics, chemistry, engineering and other branches of science and technology; for this reason several authors have studied different generalizations of the Bessel functions. In this paper the theorems of addition, multiplication and Graf's, for double index, one parameter Bessel function (Jm,n(x;τ)) are established.
Key words: Generalized Bessel functions, Addition theorem, Multiplication theorem, Graf theorem.
Texto completo disponible en PDF
Referencias
]]>[1] G. Dattoli, C. Chiccoli, S. Lorenzutta, G. Maino, M. Richetta, and A. Torre, `Advances on the Theory of Generalized Bessel Function and Applications to Multiphoton Processes´, Journal of Scientific Computing 8, 1 (1993), 69-109. [ Links ]
[2] G. Dattoli, C. Chiccoli, S. Lorenzutta, G. Maino, and A. Torre, `Generalized Bessel Functions of the Anger Type and Applications to Physical Problems´, Journal of Mathematical Analysis and Applications 184, 2 (1994), 201-221. [ Links ]
[3] G. Dattoli, S. Lorenzutta, G. Maino, A. Torre, G. Voykov, and C. Chiccoli, `Theory of Two-Index Bessel Functions and Applications to Physical Problems´, Journal of Mathematics and Physics 35, (1994), 3636-3649. [ Links ]
[4] G. Dattoli, M. Migliorati, and H. M. Srivastava, `Bessel Summation Formulae and Operational Methods´, Journal of Computational and Applied Mathematics 173, 1 (2005), 149-154. [ Links ]
[5] G. Dattoli, A. Torre, and M. Carpanese, `The Hermite - Bessel Functions: A New Point of View on the Theory of the Generalized Bessel Functions´, Radiation Physics and Chemistry 51, 3 (1998), 221-228. [ Links ]
[6] G. Dattoli, A. Torre, S. Lorenzutta, and G. Maino, `Generalized Forms of Bessel Functions and Hermite Polynomials´, Annals of Numerical Mathematics 2, (1995), 211-232. [ Links ]
[7] L. Galué, `Evaluation of Some Integrals Involving Generalized Bessel Functions´, Integral Transforms and Special Functions 12, 3 (2001), 251-256. [ Links ]
[8] L. Galué, `A Generalized Bessel Function´, Integral Transforms and Special Functions 14, 5 (2003), 395-401. [ Links ]
[9] L. Galué, H. G. Khajah, and S. L. Kalla, `Multiplication Theorems for Generalized and Double - Index Bessel Functions´, Journal of Computational and Applied Mathematics 118, 1-2 (2000), 143-150. [ Links ]
[10] S. Khan, M. A. Khan, and R. Khan, `Lie-theoretic Generating Relations Involving Multi-Variable Bessel Functions of Two Indices´, Reports on Mathematical Physics 62, 2 (2008), 183-203. [ Links ]
[11] N. N. Lebedev, Special Functions and Their Applications, Dover Publications Inc., New York, United States, 1972. [ Links ]
[12] W. A. Paciorek and G. Chapuis, `Generalized Bessel Functions in Incommensurate Structure Analysis´, Foundations of Crystallography 50, 2 (1994), 194-203. [ Links ]
[13] M. A. Pathan, A. N. Goyal, and M. J. S. Shahwan, `Lie-theoretic Generating Functions of Multivariable Generalized Bessel Functions´, Reports on Mathematical physics 39, 2 (1997), 249-254. [ Links ]
[14] H. R. Reiss and V. P. Krainov, `Generalized Bessel Functions in Tunneling Ionization´, Journal of Physics Mathematical and General 36, 20 (2003), 5575-5585. [ Links ]
Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCMv44n1a06,
AUTHOR = {Castillo, Greilyn and Galué, Leda},
TITLE = {{Teoremas para funciones de Bessel de dos índices y un parámetro}},
JOURNAL = {Revista Colombiana de Matemáticas},
YEAR = {2010}, ]]>
volume = {44},
number = {1},
pages = {65-78}
}