Matrices related to the Bell polynomials

On degenerate numbers and polynomials related to the Stirling numbers and the Bell polynomials

In this paper, we consider the degenerate numbers Rn(λ) and polynomials Rn(x, λ) related to the Stirling numbers and the Bell polynomials. We also obtain some explicit formulas for degenerate numbers Rn(λ) and polynomials Rn(x, λ). AMS subject classification: 11B68, 11S40, 11S80.

Some Identities Related to the Bell Polynomials and a Sequence of Unnamed Polynomials

In the paper, making use of two inversion theorems for the Stirling numbers and binomial coefficients, the authors present an alternative explicit formula for a sequence of unnamed polynomials, derive two identities connecting the sequence of unnamed polynomials with the Bell polynomials, and recover a known identity connecting the sequence of unnamed polynomials with the Bell polynomials. 1. M...

Laguerre-type Bell polynomials

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 gener...

Bell Polynomials of Iterated Functions

Physics can be modeled by PDEs or recursively as iterated functions. A method is presented to decompose iterated functions into Bell polynomials and then into the combinatoric structure Schroeder’s Fourth Problem. Consistency with complex dynamics is shown by deriving the classification of fixed points in complex dynamics.

Bell polynomials and Fibonacci numbers