International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 11, Pages 45423, 7 p.
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
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.