The authors provide a complete asymptotic expansion for class of functions in terms the complete
 Bell polynomials. In particular, they obtain known expansions some Keller type sequences.

A recursive relation for Bell polynomials of arbitrary order is given. Such a result is useful, in that it allows us to define a Bell polynomial of order α ∈ R without resorting to more complicated constructions, such as fractional calculus, or other methods employed in the literature. One drawback is that the recursive definition requires infinite many terms when α / ∈ R. are defined as B n (x...

The Bell number B, is the number of partitions of a finite set whose cardinality is n. The modular properties of Bell numbers have been studied by many authors. It is well known that the sequence of the residues of Bell numbers modulo any integer satisfies a linear recurrence and is periodic [ 1, 68, 13, 143. When the modulus is prime, this recurrence is particularly simple. Touchard [16] shows...

Many works have been done in recent years as to explorations for degenerate versions of some special polynomials and numbers, which began with the pioneering work Carlitz on Bernoulli Euler polynomials. This paper is focused study properties, recurrence relations identities related r-Bell polynomials, two variable Fubini r-Stirling numbers second kind. Especially, we express power series ∑n=0∞∑...