Bell polynomials and generalized Laplace transforms

ABSTRACT

An extension of the Laplace transform obtained by using the Laguerre-type exponentials is first shown. Furthermore, the solution of the Blissard problem by means of the Bell polynomials gives the possibility to associate to any numerical sequence a Laplace-type transform depending on that sequence. Computational techniques for the corresponding transform of analytic functions, involving Bell polynomials, are derived.

KEYWORDS:

• Bell polynomials
• Laguerre-type exponentials
• truncated exponentials
• Laplace transform

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 30B50
• 44A10
• 05A15
• 05A40

Acknowledgments

The author wants to thank Prof. Dr Francesco Mainardi for letting him know his work on the generalized Mittag–Leffler functions and their applications in the Laplace transform theory.

Disclosure statement

No potential conflict of interest was reported by the author(s).