International Journal of Mathematics and Mathematical Sciences 
Volume 2006 (2006), Article ID 45423, 7 pages
doi:10.1155/IJMMS/2006/45423

Laguerre-type Bell polynomials

P. Natalini1 and P. E. Ricci2

 1Dipartimento di Matematica, Università di Roma Tre, Largo S. Leonardo Murialdo 1, Roma 00146, Italy
2Dipartimento di Matematica, Università delgi Studi di Roma “La Sapienza,”, P. le Aldo Moro 2, Roma 00185, Italy
Received 14 October 2005; Revised 4 May 2006; Accepted 9 May 2006

Abstract

We develop an extension of the classical Bell polynomials introducing the Laguerre-type version of this well-known mathematical tool. The Laguerre-type Bell polynomials are useful in order to compute the nth Laguerre-type derivatives of a composite function. Incidentally, we generalize a result considered by L. Carlitz in order to obtain explicit relationships between Bessel functions and generalized hypergeometric functions.