Abstract
We prove a single sum formula for the linearization coefficients of the Bessel polynomials. In two special cases we show that our formula reduces indeed to Berg and Vignat’s formulas in their proof of the positivity results about these coefficients (Constr. Approx. 27:15–32, 2008). As a bonus we also obtain a generalization of an integral formula of Boros and Moll (J. Comput. Appl. Math. 106:361–368, 1999).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Andrews, G., Askey, R., Roy, R.: Special Functions. Encyclopedia of Mathematics and Its Applications, vol. 71. Cambridge University Press, Cambridge (1999)
Berg, C., Vignat, C.: Linearization coefficients of Bessel polynomials and properties of student t-distributions. Constr. Approximation 27, 15–32 (2008)
Berg, C., Vignat, C.: Derivation of an integral of Boros and Moll via convolution of student t-densities. To appear in Ramanujan J. doi:10.1007/s11139-010-9279-5
Boros, G., Moll, V.H.: An integral hidden in Gradshteyn and Ryzhik. J. Comput. Appl. Math. 106, 361–368 (1999)
Carlitz, L.: A note on the Bessel polynomials. Duke Math. J. 24, 151–162 (1957)
Grosswald, E.: Bessel Polynomials. Lecture Notes in Mathematics, vol. 698. Springer, New York (1978)
Rainville, E.D.: Special Funtions. Macmillan Company, New York (1960)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Atia, M.J., Zeng, J. An explicit formula for the linearization coefficients of Bessel polynomials. Ramanujan J 28, 211–221 (2012). https://doi.org/10.1007/s11139-011-9348-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11139-011-9348-4